scholarly journals SALLY MODULES AND REDUCTION NUMBERS OF IDEALS

2016 ◽  
Vol 226 ◽  
pp. 106-126 ◽  
Author(s):  
L. GHEZZI ◽  
S. GOTO ◽  
J. HONG ◽  
W. V. VASCONCELOS
Keyword(s):  
Local Ring ◽  
Complete Intersection ◽  
Primary Ideal ◽  
Two Dimensional ◽  
Fiber Ring ◽  
Reduction Number ◽  
Explicit Realization ◽  
The Relationship ◽  
The Way

We study the relationship between the reduction number of a primary ideal of a local ring relative to one of its minimal reductions and the multiplicity of the corresponding Sally module. This paper is focused on three goals: (i) to develop a change of rings technique for the Sally module of an ideal to allow extension of results from Cohen–Macaulay rings to more general rings; (ii) to use the fiber of the Sally modules of almost complete intersection ideals to connect its structure to the Cohen–Macaulayness of the special fiber ring; (iii) to extend some of the results of (i) to two-dimensional Buchsbaum rings. Along the way, we provide an explicit realization of the $S_{2}$-fication of arbitrary Buchsbaum rings.

Reduction numbers and Hilbert polynomials of ideals in higher dimensional CohenMacaulay local rings

1992 ◽  
Vol 111 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Yinghwa Wu
Keyword(s):  
Local Ring ◽  
Residue Field ◽  
Primary Ideal ◽  
Local Rings ◽  
Hilbert Polynomials ◽  
Higher Dimensional ◽  
Reduction Number ◽  
Minimal Reduction ◽  
System Of Parameters

Throughout, (R, m) will denote a d-dimensional CohenMacaulay (CM for short) local ring having an infinite residue field and I an m-primary ideal in R. Recall that an ideal J I is said to be a reduction of I if Ir+1 = JIr for some r 0, and a reduction J of I is called a minimal reduction of I if J is generated by a system of parameters. The concepts of reduction and minimal reduction were first introduced by Northcott and Rees12. If J is a reduction of I, define the reduction number of I with respect to J, denoted by rj(I), to be min {r 0 Ir+1 = JIr}. The reduction number of I is defined as r(I) = min {rj(I)J is a minimal reduction of I}. The reduction number r(I) is said to be independent if r(I) = rj(I) for every minimal reduction J of I.

On Special Fiber Rings of Modules

2019 ◽  
Vol 72 (1) ◽  
pp. 225-242
Author(s):  
Cleto B. Miranda-Neto
Keyword(s):  
Local Ring ◽  
Arbitrary Dimension ◽  
Residue Field ◽  
Independent Interest ◽  
General Situation ◽  
Finitely Generated ◽  
Fiber Ring ◽  
Noetherian Local Ring ◽  
Reduction Number

AbstractWe prove results concerning the multiplicity as well as the Cohen–Macaulay and Gorenstein properties of the special fiber ring $\mathscr{F}(E)$ of a finitely generated $R$-module $E\subsetneq R^{e}$ over a Noetherian local ring $R$ with infinite residue field. Assuming that $R$ is Cohen–Macaulay of dimension 1 and that $E$ has finite colength in $R^{e}$, our main result establishes an asymptotic length formula for the multiplicity of $\mathscr{F}(E)$, which, in addition to being of independent interest, allows us to derive a Cohen–Macaulayness criterion and to detect a curious relation to the Buchsbaum–Rim multiplicity of $E$ in this setting. Further, we provide a Gorensteinness characterization for $\mathscr{F}(E)$ in the more general situation where $R$ is Cohen–Macaulay of arbitrary dimension and $E$ is not necessarily of finite colength, and we notice a constraint in terms of the second analytic deviation of the module $E$ if its reduction number is at least three.

The Joint Reduction Number and Upper Bounds of Hilbert Series of Fiber Cones

2013 ◽  
Vol 20 (04) ◽  
pp. 653-662
Author(s):  
Guangjun Zhu
Keyword(s):  
Local Ring ◽  
Upper Bound ◽  
Hilbert Series ◽  
Upper Bounds ◽  
Primary Ideal ◽  
Reduction Number ◽  
Joint Reduction

Let (R,𝔪) be a Cohen-Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R and K an ideal containing I. Let a1,…,ad be a joint reduction of (I[d-1]|K), and set L=(a1,…,ad), J=(a1,…,ad-1). When depth G(I) ≥ d-1 and depth FK(I) ≥ d-2, we show that the lengths [Formula: see text], [Formula: see text] and the joint reduction number rL(I|K) are independent of L. In the general case, we give an upper bound of the Hilbert series of FK(I). When depth G(I) ≥ d-1, we also provide a characterization, in terms of the Hilbert series of FK(I), of the condition depth FK(I) ≥ d-1.

scholarly journals On Fiber Cones of 𝑚-Primary Ideals

2007 ◽  
Vol 59 (1) ◽  
pp. 109-126 ◽  
Author(s):  
A. V. Jayanthan ◽  
Tony J. Puthenpurakal ◽  
J. K. Verma
Keyword(s):  
Local Ring ◽  
Primary Ideal ◽  
Reduction Number ◽  
Fiber Cone ◽  
Minimal Reduction ◽  
Primary Ideals

AbstractTwo formulas for the multiplicity of the fiber cone of an 𝑚-primary ideal of a d-dimensional Cohen–Macaulay local ring (R, 𝑚) are derived in terms of the mixed multiplicity ed–1(𝑚|I), the multiplicity e(I), and superficial elements. As a consequence, the Cohen–Macaulay property of F(I) when I has minimal mixed multiplicity or almost minimal mixed multiplicity is characterized in terms of the reduction number of I and lengths of certain ideals. We also characterize the Cohen–Macaulay and Gorenstein properties of fiber cones of 𝑚–primary ideals with a d–generated minimal reduction J satisfying ℓ(I2/JI) = 1 or ℓ(I𝑚/J𝑚) = 1.

The time(s) of the photographed

2019 ◽  
Vol 10 (2) ◽  
pp. 195-206 ◽  
Author(s):  
Reza Tavakol
Keyword(s):  
Optical Receiver ◽  
Two Dimensional ◽  
Temporal Effects ◽  
Space And Time ◽  
Optical Images ◽  
Severe Reduction ◽  
The Subject ◽  
The Relationship ◽  
The Universe ◽  
The Way

The relationship between the photographic and optical images and time has been the subject of great deal of debate. Despite their differences, what many of these considerations have in common is their focus on the receiver, whether mechanical (the camera), biological (the eye‐brain as the optical receiver), social or the memory and imagination of the observer. My aim here is to shift the emphasis from the receiver to the object or vista that is photographed or viewed and to explore how the constraints implied by our modern understanding of the Universe, concerning space and time, impact on the way we perceive photographic and optical images. Viewed from this perspective, photographs can be treated as light projections of sections of the four-dimensional observable world onto two-dimensional spatial photographic or viewing surfaces. I shall show that despite the severe reduction that such projections imply, these modern considerations have the important consequence of bestowing a complex temporality upon optical images, including photographs. This realization dramatically changes the way we view photographs. I give examples of this rich temporality through considerations of terrestrial images ‐ and more significantly images of the Sky, where these temporal effects are far more pronounced.

The Type of Temperament, Mood, and Strategies of Categorization

2012 ◽  
Vol 33 (4) ◽  
pp. 227-236 ◽  
Author(s):  
Agata Wytykowska
Keyword(s):  
Information Processing ◽  
Negative Mood ◽  
Cognitive Activity ◽  
Processing Capacity ◽  
Affective Value ◽  
The Relationship ◽  
The Way

In Strelau’s theory of temperament (RTT), there are four types of temperament, differentiated according to low vs. high stimulation processing capacity and to the level of their internal harmonization. The type of temperament is considered harmonized when the constellation of all temperamental traits is internally matched to the need for stimulation, which is related to effectiveness of stimulation processing. In nonharmonized temperamental structure, an internal mismatch is observed which is linked to ineffectiveness of stimulation processing. The three studies presented here investigated the relationship between temperamental structures and the strategies of categorization. Results revealed that subjects with harmonized structures efficiently control the level of stimulation stemming from the cognitive activity, independent of the affective value of situation. The pattern of results attained for subjects with nonharmonized structures was more ambiguous: They were as good as subjects with harmonized structures at adjusting the way of information processing to their stimulation processing capacities, but they also proved to be more responsive to the affective character of stimulation (positive or negative mood).

Understanding prescription in language. A corpus-based approach

2019 ◽  
Vol 41 (2) ◽  
pp. 67-81
Author(s):  
Douglas A. Kibbee ◽  
Alan Craig
Keyword(s):  
Social Context ◽  
French Tradition ◽  
Linguistic Behavior ◽  
The Relationship ◽  
The Way

We define prescription as any intervention in the way another person speaks. Long excluded from linguistics as unscientific, prescription is in fact a natural part of linguistic behavior. We seek to understand the logic and method of prescriptivism through the study of usage manuals: their authors, sources and audience; their social context; the categories of “errors” targeted; the justification for correction; the phrasing of prescription; the relationship between demonstrated usage and the usage prescribed; the effect of the prescription. Our corpus is a collection of about 30 usage manuals in the French tradition. Eventually we hope to create a database permitting easy comparison of these features.

On (Not) Translating Lacan: Barbara Cassin's Sophistico-Analytical Performances

Paragraph ◽  
2020 ◽  
Vol 43 (1) ◽  
pp. 98-113
Author(s):  
Michael Syrotinski
Keyword(s):  
Machine Translation ◽  
Reading And Writing ◽  
The Relationship ◽  
The Way

Barbara Cassin's Jacques the Sophist: Lacan, Logos, and Psychoanalysis, recently translated into English, constitutes an important rereading of Lacan, and a sustained commentary not only on his interpretation of Greek philosophers, notably the Sophists, but more broadly the relationship between psychoanalysis and sophistry. In her study, Cassin draws out the sophistic elements of Lacan's own language, or the way that Lacan ‘philosophistizes’, as she puts it. This article focuses on the relation between Cassin's text and her better-known Dictionary of Untranslatables, and aims to show how and why both ‘untranslatability’ and ‘performativity’ become keys to understanding what this book is not only saying, but also doing. It ends with a series of reflections on machine translation, and how the intersubjective dynamic as theorized by Lacan might open up the possibility of what is here termed a ‘translatorly’ mode of reading and writing.

Klein with Lacan: A Study on the Reception of Lacanian Ideas in Uruguay and Its Effects on Clinical Practices (1955–82)

2020 ◽  
Vol 22 (3) ◽  
pp. 341-361
Author(s):  
Gonzalo Grau-Pérez ◽  
J. Guillermo Milán
Keyword(s):  
Clinical Practice ◽  
Clinical Material ◽  
Clinical Practices ◽  
Before And After ◽  
The Difference ◽  
The 1960S ◽  
The Relationship ◽  
Discursive Approach ◽  
The Way ◽  
Clinical Cases

In Uruguay, Lacanian ideas arrived in the 1960s, into a context of Kleinian hegemony. Adopting a discursive approach, this study researched the initial reception of these ideas and its effects on clinical practices. We gathered a corpus of discursive data from clinical cases and theoretical-doctrinal articles (from the 1960s, 1970s and 1980s). In order to examine the effects of Lacanian ideas, we analysed the difference in the way of interpreting the clinical material before and after Lacan's reception. The results of this research illuminate some epistemological problems of psychoanalysis, especially the relationship between theory and clinical practice.

FBI and Religion

2017 ◽  
Keyword(s):  
Religious Orientation ◽  
Religious Communities ◽  
Academic Scholarship ◽  
History Of ◽  
Interdisciplinary Assessment ◽  
Civic Religion ◽  
New Research ◽  
The Relationship ◽  
The Way

This volume is an interdisciplinary assessment of the relationship between religion and the FBI. We recount the history of the FBI’s engagement with multiple religious communities and with aspects of public or “civic” religion such as morality and respectability. The book presents new research to explain roughly the history of the FBI’s interaction with religion over approximately one century, from the pre-Hoover period to the post-9/11 era. Along the way, the book explores vexed issues that go beyond the particulars of the FBI’s history—the juxtaposition of “religion” and “cult,” the ways in which race can shape the public’s perceptions of religion (and vica versa), the challenges of mediating between a religious orientation and a secular one, and the role and limits of academic scholarship as a way of addressing the differing worldviews of the FBI and some of the religious communities it encounters.

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