Related papers: Ideals and finiteness conditions for subsemigroups
Using graph-theoretic techniques for f.g. subgroups of $F^{\mathbb{Z}[t]}$ we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked…
We consider the general question of how the homological finiteness property left-FPn holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. In particular we show that left-FPn is…
A left almost semigroup (LA-semigroup) or an Abel-Grassmann's groupoid (AG-groupoid) is investigated in several papers. In this paper we have discussed ideals in LA-semigroups. Specifically, we have shown that every ideal in an LA-semigroup…
In a couple of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In this article, we introduce and examine…
A semigroup variety V is said to be locally K-finite, where K stands for any of Green's relations H, R, L, D, or J, if every finitely generated semigroup from V has only finitely many K-classes. We characterize locally K-finite varieties of…
In this paper, we characterize intra-regular LA-semihypergroups by using the properties of their left and right hyperideals and we investigate some useful conditions for an LA-semihypergroup to become an intra-regular LA-semihypergroup.
We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i) |N_G(H):H| is finite for every non-normal subgroup H of G, and (ii) |C_G(x):<x>| is finite for every non-normal cyclic subgroup <x> of G.…
Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of…
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…
We consider various decision problems for automatic semigroups, which involve the provision of an automatic structure as part of the problem instance. With mild restrictions on the automatic structure, which seem to be necessary to make the…
A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes.…
In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we classify finite semigroups such that the…
Ideal series of semigroups play an important role in the examination of semigroups which have proper two-sided ideals. But the corresponding theorems cannot be used when left simple (or right simple or simple) semigroups are considered. So…
This paper studies algebraic residual intersections in rings with Serre's condition \( S_{s} \). It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a…
We construct `structure invariants' of a one-ended, finitely presented group that describe the way in which the factors of its JSJ decomposition over two-ended subgroups fit together. For groups satisfying two technical conditions, these…
In this paper we introduce the notion of right waist and right comparizer ideals for semigroups. In particular, we study the ideal theory of semigroups containing right waists and right comparizer ideals. We also study those properties of…
Good semigroups form a class of submonoids of $\mathbb{N}^d$ containing the value semigroups of curve singularities. In this article, we describe a partition of the complements of good semigroup ideals, having as main application the…
We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$, either $\{x,y\}$ is contained in a minimal generating set for $G$ or one of $x$ and $y$ is a power of the other.…
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.
Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if $C_G(N) \leq N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing…