On p -quaternionic pairings of non-elementary type

2000 ◽  
Vol 101 (1) ◽  
pp. 39-47 ◽  
Author(s):  
M. Kula
Keyword(s):  
Elementary Type

Agent-Based Computational Model

2017 ◽  
Author(s):  
Joshua M. Epstein
Keyword(s):  
Computational Model ◽  
Bounded Rationality ◽  
Time Scales ◽  
Spatially Explicit ◽  
Agent Based ◽  
Affective Component ◽  
Elementary Type ◽  
Social Component ◽  
Different Time Scales

This part describes the agent-based and computational model for Agent_Zero and demonstrates its capacity for generative minimalism. It first explains the replicability of the model before offering an interpretation of the model by imagining a guerilla war like Vietnam, Afghanistan, or Iraq, where events transpire on a 2-D population of contiguous yellow patches. Each patch is occupied by a single stationary indigenous agent, which has two possible states: inactive and active. The discussion then turns to Agent_Zero's affective component and an elementary type of bounded rationality, as well as its social component, with particular emphasis on disposition, action, and pseudocode. Computational parables are then presented, including a parable relating to the slaughter of innocents through dispositional contagion. This part also shows how the model can capture three spatially explicit examples in which affect and probability change on different time scales.

scholarly journals Demuškin groups, Galois modules, and the Elementary Type Conjecture

2006 ◽  
Vol 304 (2) ◽  
pp. 1130-1146 ◽  
Author(s):  
John Labute ◽  
Nicole Lemire ◽  
Ján Mináč ◽  
John Swallow
Keyword(s):  
Elementary Type ◽  
Galois Modules

Graded witt rings of elementary type

1985 ◽  
Vol 272 (2) ◽  
pp. 267-280 ◽  
Author(s):  
J�n Kr. Arason ◽  
Richard Elman ◽  
Bill Jacob
Keyword(s):  
Witt Rings ◽  
Elementary Type

Abstract Witt Rings When Certain Binary Forms Represent Exactly Four Elements

1993 ◽  
Vol 45 (6) ◽  
pp. 1184-1199 ◽  
Author(s):  
Craig M. Cordes
Keyword(s):  
Group Ring ◽  
Positive Characteristic ◽  
Finitely Generated ◽  
Binary Forms ◽  
Witt Ring ◽  
Witt Rings ◽  
Elementary Type ◽  
Characteristic 2

AbstractAn abstract Witt ring (R, G) of positive characteristic is known to be a group ring S[Δ] with ﹛1﹜ ≠ Δ ⊆ G if and only if it contains a form〈1,x〉, x ≠1, which represents only the two elements 1 and x. Carson and Marshall have characterized all Witt rings of characteristic 2 which contain binary forms representing exactly four elements. Such results which show R is isomorphic to a product of smaller rings are helpful in settling the conjecture that every finitely generated Witt ring is of elementary type. Here, some special situations are considered. In particular if char(R) = 8, |D〈l, 1〉| = 4, and R contains no rigid elements, then R is isomorphic to the Witt ring of the 2-adic numbers. If char(R) = 4, |D〈l,a〉| = 4 where a ∈ D〈1, 1〉, and R contains no rigid elements, then R is either a ring of order 8 or is the specified product of two Witt rings at least one of which is a group ring. In several cases R is realized by a field.

Gorenstein Witt Rings

1988 ◽  
Vol 40 (5) ◽  
pp. 1186-1202 ◽  
Author(s):  
Robert W. Fitzgerald
Keyword(s):  
Group Ring ◽  
Quotient Ring ◽  
Injective Resolution ◽  
Gorenstein Rings ◽  
Witt Ring ◽  
Witt Rings ◽  
Local Type ◽  
Elementary Type ◽  
Ring Extensions

Throughout R is a noetherian Witt ring. The basic example is the Witt ring WF of a field F of characteristic not 2 and finite. We study the structure of (noetherian) Witt rings which are also Gorenstein rings (i.e., have a finite injective resolution). The underlying motivation is the elementary type conjecture. The Gorenstein Witt rings of elementary type are group ring extensions of Witt rings of local type. We thus wish to compare the two classes of Witt rings: Gorenstein and group ring over local type. We show the two classes enjoy many of the same properties and are, in several cases, equal. However we cannot decide if the two classes are always equal.In the first section we consider formally real Witt rings R (equivalently, dim R = 1). Here the total quotient ring of R is R-injective if and only if R is reduced. Further, R is Gorenstein if and only if R is a group ring over Z. This result appears to be somewhat deep.

Classical History between Epic and Rhetoric

Why History? ◽  
2020 ◽  
pp. 16-44
Author(s):  
Donald Bloxham
Keyword(s):  
Historical Change ◽  
Power Structures ◽  
Classical Scholarship ◽  
Elementary Type ◽  
Classical Models ◽  
Historical Truth ◽  
The Relationship ◽  
Classical History

This chapter establishes the foundations on which the rest of the book is built since post-classical scholarship largely develops from classical models or is shaped by its reaction against those models. The chapter addresses a series of conceptual issues that have recurring relevance, including: differing conceptions of the nature of historical truth; the relationship between History and ethnography; the relationship between rhetoric and historianship; the relationship between philosophy, poetry, and History; and the relationship between ‘useful’ and ‘pleasurable’ Histories. In a more empirical vein the chapter discusses the relationship between Greek and Roman historianship and accounts for different tendencies in the development of historiography in each culture—tendencies like a greater or lesser interest in the outside world, and a greater or lesser interest in individuals as opposed to power structures or the study of society and culture. The question of the consciousness of qualitative historical change is also discussed in the case of a number of historians. In the 900 or so years of historianship covered in this chapter no rationale for History that is present at or near the outset was ruled out by the end, though of course many avenues of possibility were more fully explored. It is more than coincidence that the survey opens and closes with species of History as Identity, beginning with the most elementary type of that genre: genealogy.

scholarly journals One-Relator Maximal Pro-p Galois Groups and the Koszulity Conjectures

2020 ◽  
Author(s):  
Claudio Quadrelli
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Group Algebra ◽  
Galois Groups ◽  
Cohomology Algebra ◽  
Augmentation Ideal ◽  
Graded Algebra ◽  
Absolute Galois Group ◽  
Quadratic Algebras ◽  
Elementary Type

Abstract Let p be a prime number and let ${\mathbb{K}}$ be a field containing a root of 1 of order p. If the absolute Galois group $G_{\mathbb{K}}$ satisfies $\dim\, H^1(G_{\mathbb{K}},\mathbb{F}_p)\lt\infty$ and $\dim\, H^{\,2}(G_{\mathbb{K}},\mathbb{F}_p)=1$, we show that L. Positselski’s and T. Weigel’s Koszulity conjectures are true for ${\mathbb{K}}$. Also, under the above hypothesis, we show that the $\mathbb{F}_p$-cohomology algebra of $G_{\mathbb{K}}$ is the quadratic dual of the graded algebra ${\rm gr}_\bullet\mathbb{F}_p[G_{\mathbb{K}}]$, induced by the powers of the augmentation ideal of the group algebra $\mathbb{F}_p[G_{\mathbb{K}}]$, and these two algebras decompose as products of elementary quadratic algebras. Finally, we propose a refinement of the Koszulity conjectures, analogous to I. Efrat’s elementary type conjecture.

Gorenstein Witt Rings II

1997 ◽  
Vol 49 (3) ◽  
pp. 499-519
Author(s):  
Robert W. Fitzgerald
Keyword(s):  
Classification Problem ◽  
Witt Rings ◽  
Dimension Zero ◽  
Elementary Type

AbstractThe abstract Witt rings which are Gorenstein have been classified when the dimension is one and the classification problem for those of dimension zero has been reduced to the case of socle degree three. Here we classify the Gorenstein Witt rings of fields with dimension zero and socle degree three. They are of elementary type.

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