Regularity of Growth and the Class S

Arens regularity of inverse semigroup algebras‎

‎We present a characterization of Arens regular semigroup algebras‎ ‎$ell^1(S)$‎, ‎for a large class of semigroups‎. ‎Mainly‎, ‎we show that‎ ‎if the set of idempotents of an inverse semigroup $S$ is finite‎, ‎then $ell^1(S)$ is Arens regular if and only if $S$ is finite‎.

$(m,n)$-Hyperideals in Ordered Semihypergroups

In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideal...

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs

An upper bound for the regularity of powers of edge ideals

‎A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$‎, ‎denoted by match$(G)$‎. ‎In this paper‎, ‎we provide a generalization of this result for powers of edge ideals‎. ‎More precisely‎, ‎we show that for every graph $G$ and every $sgeq 1$‎, ‎$${rm reg}( R‎/ ‎I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...

On Regularity of Acts

In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We als...