n-Matlis cotorsion modules and n-matlis domains

2019 ◽  
Vol 19 (07) ◽  
pp. 2050139
Author(s):  
Yongyan Pu ◽  
Gaohua Tang ◽  
Fanggui Wang
Keyword(s):  
Projective Dimension ◽  
Negative Integer ◽  
Dimension Formula

Let [Formula: see text] be a domain with its field [Formula: see text] of quotients, [Formula: see text] an [Formula: see text]-module and [Formula: see text] a fixed non-negative integer. Then [Formula: see text] is called [Formula: see text]-Matlis cotorsion if [Formula: see text] for any integer [Formula: see text]. Also [Formula: see text] is said to be [Formula: see text]-Matlis flat if [Formula: see text] for any [Formula: see text]-Matlis cotorsion [Formula: see text]-module [Formula: see text]. We proved that [Formula: see text] is a complete hereditary cotorsion theory, where [Formula: see text] (respectively, [Formula: see text]) denotes the class of all [Formula: see text]-Matlis flat (respectively, [Formula: see text]-Matlis cotorsion) [Formula: see text]-modules. In this paper, it is proved that [Formula: see text] is an [Formula: see text]-Matlis domain if and only if epic images of [Formula: see text]-Matlis cotorsion [Formula: see text]-modules are again [Formula: see text]-Matlis cotorsion if and only if [Formula: see text]-Matlis flat [Formula: see text]-modules are of projective dimension [Formula: see text] if and only if [Formula: see text] if and only if [Formula: see text].

Semidualizing bimodules and related Gorenstein homological dimensions

2016 ◽  
Vol 15 (10) ◽  
pp. 1650193 ◽  
Author(s):  
Aimin Xu ◽  
Nanqing Ding
Keyword(s):  
Projective Dimension ◽  
Negative Integer ◽  
Homological Dimensions ◽  
Semidualizing Bimodule ◽  
Finitely Presented

Let [Formula: see text] be a semidualizing bimodule with [Formula: see text] left coherent and [Formula: see text] right coherent. For a non-negative integer [Formula: see text], it is shown that [Formula: see text]-[Formula: see text]-[Formula: see text] if and only if every finitely presented left [Formula: see text]-module has [Formula: see text]-projective dimension at most [Formula: see text] if and only if every finitely presented right [Formula: see text]-module has [Formula: see text]-projective dimension at most [Formula: see text]. As applications, some well-known results are extended.

scholarly journals Relative global Gorenstein dimensions

2021 ◽  
pp. 2250208
Author(s):  
Víctor Becerril
Keyword(s):  
Admissible Pair ◽  
Abelian Category ◽  
Projective Dimension ◽  
Dimension Formula

Let [Formula: see text] be an abelian category. In this paper, we investigate the global [Formula: see text]-Gorenstein projective dimension [Formula: see text], associated to a GP-admissible pair [Formula: see text]. We give homological conditions over [Formula: see text] that characterize it. Moreover, given a GI-admissible pair [Formula: see text], we study conditions under which [Formula: see text] and [Formula: see text] are the same.

scholarly journals Triangulated Matlis equivalence

2018 ◽  
Vol 17 (04) ◽  
pp. 1850067 ◽  
Author(s):  
Leonid Positselski
Keyword(s):  
Commutative Ring ◽  
Projective Dimension ◽  
Derived Categories ◽  
Multiplicative System ◽  
Module Category ◽  
Dimension Formula ◽  
Abelian Categories ◽  
Torsion Modules ◽  
Cohomology Modules

This paper is a sequel to [L. Positselski, Dedualizing complexes and MGM duality, J. Pure Appl. Algebra 220(12) (2016) 3866–3909, arXiv:1503.05523 [math.CT]; Contraadjusted modules, contramodules, and reduced cotorsion modules, preprint (2016), arXiv:1605.03934 [math.CT]]. We extend the classical Harrison–Matlis module category equivalences to a triangulated equivalence between the derived categories of the abelian categories of torsion modules and contramodules over a Matlis domain. This generalizes to the case of any commutative ring [Formula: see text] with a fixed multiplicative system [Formula: see text] such that the [Formula: see text]-module [Formula: see text] has projective dimension [Formula: see text]. The latter equivalence connects complexes of [Formula: see text]-modules with [Formula: see text]-torsion and [Formula: see text]-contramodule cohomology modules. It takes a nicer form of an equivalence between the derived categories of abelian categories when [Formula: see text] consists of nonzero-divisors or the [Formula: see text]-torsion in [Formula: see text] is bounded.

scholarly journals Directed unions of local monoidal transforms and GCD domains

2019 ◽  
Vol 19 (04) ◽  
pp. 2050061
Author(s):  
Lorenzo Guerrieri
Keyword(s):  
Prime Ideal ◽  
Local Ring ◽  
Maximal Ideal ◽  
General Setting ◽  
Regular Local Ring ◽  
Dimension Formula

Let [Formula: see text] be a regular local ring of dimension [Formula: see text]. A local monoidal transform of [Formula: see text] is a ring of the form [Formula: see text], where [Formula: see text] is a regular parameter, [Formula: see text] is a regular prime ideal of [Formula: see text] and [Formula: see text] is a maximal ideal of [Formula: see text] lying over [Formula: see text] In this paper, we study some features of the rings [Formula: see text] obtained as infinite directed union of iterated local monoidal transforms of [Formula: see text]. In order to study when these rings are GCD domains, we also provide results in the more general setting of directed unions of GCD domains.

scholarly journals A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases

2021 ◽  
Vol 96 ◽  
pp. 545-558
Author(s):  
Paulo Roberto Prezotti Filho ◽  
Valderio Anselmo Reisen ◽  
Pascal Bondon ◽  
Márton Ispány ◽  
Milena Machado Melo ◽  
...  
Keyword(s):  
Time Series ◽  
Statistical Model ◽  
Respiratory Diseases ◽  
Negative Integer

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA

1995 ◽  
Vol 09 (12) ◽  
pp. 1429-1451 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Fractal Dimension ◽  
Lattice Dynamics ◽  
Nearest Neighbor ◽  
Average Distance ◽  
Local Maximum ◽  
Fractal Dimensions ◽  
Dimension Formula ◽  
Phonon Spectra ◽  
Wide Range ◽  
Silver Mean

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

Analytical method for optimum non‐negative integer bit allocation

2016 ◽  
Vol 10 (8) ◽  
pp. 936-946 ◽  
Author(s):  
Mahdi Hatam ◽  
Mohammad Ali Masnadi‐Shirazi
Keyword(s):  
Analytical Method ◽  
Negative Integer ◽  
Bit Allocation

Modules of finite projective dimension and cocovers

1996 ◽  
Vol 306 (1) ◽  
pp. 445-457 ◽  
Author(s):  
Dieter Happel ◽  
Luise Unger
Keyword(s):  
Projective Dimension ◽  
Finite Projective Dimension
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