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EQUIVARIANT FLOW EQUIVALENCE FOR SHIFTS OF FINITE TYPE,BY MATRIX EQUIVALENCE OVER GROUP RINGS
EQUIVARIANT FLOW EQUIVALENCE SHIFTS OF FINITE TYPE MATRIX EQUIVALENCE OVER GROUP RINGS
2015/9/29
Let G be a finite group. We classify G-equivariant flow equivalence of nontrivial irreducible shifts of finite type interms of (i) elementary equivalence of matrices over ZG and (ii) the conjugacy cla...
Topologizing Rings of Map Germs: An Order Theoretic Analysis of Germs via Nonstandard Methods
map germ topology nonstandard
2012/6/19
Using nonstandard analysis we define a topology on the ring of germs of functions: $(mathbb R^n,0)\rightarrow(mathbb R,0)$. We prove that this topology is absolutely convex, Hausdorff, that convergent...
Large self-injective rings and the generating hypothesis
Large self-injective rings the generating hypothesis Algebraic Topology
2012/6/9
We construct a number of different examples of non-Noetherian graded rings that are injective as modules over themselves (or have some related but weaker properties). We discuss how these are related ...
Brauer's generalized decomposition numbers and universal deformation rings
Universal deformation rings Brauer’s generalized decomposition numbers tame blocks dihedral defect groups semidihedral defect groups
2012/4/17
We study the problem of lifting to local rings certain mod 2 representations V of finite groups G which belong to 2-modular tame blocks B of G having at least two isomorphism classes of simple modules...
On the Koszul property of toric face rings
Koszul property toric face rings Commutative Algebra
2011/9/19
Abstract: Toric face rings is a generalization of the concepts of affine semigroup rings and Stanley-Reisner rings. We characterize toric face rings having the Koszul, strongly Koszul or initially Kos...
Vanishing of Tate homology and depth formulas over local rings
AB ring complete intersection ring depth formula Gorenstein ring rigidity of Tor Tate homology
2011/9/9
Abstract: Auslander's depth formula for pairs of Tor-independent modules over a regular local ring,
depth(M \otimes N) = depth(M) + depth(N) - depth(R),
has been generalized in several directions ...
The Kaplansky condition and rings of almost stable range 1
almost stable range 1 elementary divisor ring Kaplansky condition K-Hermite stable range
2011/9/9
Abstract: We present some variants of the Kaplansky condition for a K-Hermite ring $R$ to be an elementary divisor ring; for example, a commutative K-Hermite ring $R$ is an EDR iff for any elements $x...
Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings
Poisson Ideals Cluster Algebras the Spectra of Quantized Coordinate Rings Quantum Algebra
2011/9/6
Abstract: We describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster ...
Two questions of L. Va${\rm \check{\textbf{s}}}$ on *-clean rings
Clean ring Clean ring Regular ring Strongly clean ring Unit regular ring
2011/8/26
Abstract: A ring $R$ with an involution * is called (strongly) *-clean if every element of $R$ is the sum of a unit and a projection (that commute). All *-clean rings are clean. Va${\rm \check{s}}$ [L...
Rings over which every module has a flat $δ$-cover
-covers -perfect rings -semiperfect rings Flat modules
2011/8/25
Abstract: Let $M$ be a module. A {\em $\delta$-cover} of $M$ is an epimorphism from a module $F$ onto $M$ with a $\delta$-small kernel. A $\delta$-cover is said to be a {\em flat $\delta$-cover} in ca...
$n$-strongly Gorenstein rings
strongly (n-)Gorenstein projective injective modules Gorenstein global dimensions
2011/8/24
Abstract: This paper introduces and studies a particular subclass of the class of commutative rings with finite Gorenstein global dimension.
On a Conjecture on the weak global dimension of Gaussian rings
Gaussian rings weak dimension content non-noetherian rings
2011/8/24
Abstract: Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is 0,1 or \infty. In this paper, we prove their conjecture in all cases except when R is a non-reduced local Gau...
Abstract: A ring $R$ is called right SSP (SIP) if the sum (intersection) of any two direct summands of $R_{R}$ is also a direct summand. Left sides can be defined similarly. The following are equivale...
Generalized derivations on Lie ideals in prime rings
Derivations Lie ideals generalized derivations centralizing mappings prime rings
2011/4/6
Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for...
Cohomology rings of good contact toric manifolds
contact toric cohomology equivariant cohomology
2011/1/20
A good contact toric manifold M is determined by its moment cone C. We compute the equivariant cohomology ring with Z coefficient of M in terms of the combinatorial data of C. Then under a smoothness ...