Related papers: Ideals in intra-regular left almost semigroups

Let $S,T$ be two numerical semigroups. We study when $S$ is one half of $T$, with $T$ almost symmetric. If we assume that the type of $T$, $t(T)$, is odd, then for any $S$ there exist infinitely many such $T$ and we prove that $1 \leq t(T)…

The paper is an overview of recent results on algebraic structures (semigroups, groupoids, algebras, inverse semigroups, and groups) associated with objects with a rich set of partial symmetries. We discuss etale groupoids and inverse…

In the current paper we study the groups, whose subnormal abelian subgroups are normal. We obtained a quite detailed description of such hyperabelian groups with a periodic Baer radical. The description of hyperabelian Lie algebras, whose…

Let ${\cal M}(S; \Lambda; P)$ denote a Rees $I\times \Lambda$ matrix semigroup without zero over a semigroup $S$, where $I$ is a singleton. If $\theta _S$ denotes the kernel of the right regular representation of a semigroup $S$, then a…

This paper introduces a notion of presentation for locally inverse semigroups and develops a graph structure to describe the elements of locally inverse semigroups given by these presentations. These graphs will have a role similar to the…

In this paper for a noetherian ring R with nilradical N we define semiprime ideals P and Q called as the left and right krull homogenous parts of N . We also recall the known definitions of localisability and the weak ideal invariance…

Let (G, *) be a semigroup, D subset of G, and n >= 2 be an integer. We say that (D, *) is an n-closed subset of G if a_1* ... *a_n in D for every a_1, ..., a_n in D. Hence every closed set is a 2-closed set. The concept of n-closed sets…

We consider the "intrinsic" symmetry group of a two-component link $L$, defined to be the image $\Sigma(L)$ of the natural homomorphism from the standard symmetry group $\MCG(S^3,L)$ to the product $\MCG(S^3) \cross \MCG(L)$. This group,…

Lee and Kwon [12] defined an ordered semigroup S to be completely regular if a 2 (a2Sa2] for every a 2 S. We characterize every completely regular ordered semigroup as a union of t-simple subsemigroups, and every Clifford ordered semigroup…

Let $S$ be a semigroup, $\Lambda$ a non-empty set and $P$ a mapping of $\Lambda$ into $S$. The set $S\times \Lambda$ together with the operation $\circ _P$ defined by $(s, \lambda)\circ _P(t, \mu )=(sP(\lambda)t, \mu )$ form a semigroup…

Let kG be the completed group algebra of a uniform pro-p group G with coefficients in a field k of characteristic p. We study right ideals I in kG that are invariant under the action of another uniform pro-p group Gamma. We prove that if I…

We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of…

In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…

The left-ideal relation graph on a ring $R$, denoted by $\overrightarrow{\Gamma_{l-i}}(R)$, is a directed graph whose vertex set is all the elements of $R$ and there is a directed edge from $x$ to a distinct $y$ if and only if the left…

Let $R$ be a noncommutative ring, and let $S$ be an $m$-system of $R$. In this paper, we give more results on the concept of almost prime (right) ideals, that were introduced by the first two authors, especially in (right) $S$-unital rings,…

We investigate the minimal number of generators $\mu$ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the…

Let $X$ be a finite set such that $|X|=n$ and let $i\leq j \leq n$. A group $G\leq \sym$ is said to be $(i,j)$-homogeneous if for every $I,J\subseteq X$, such that $|I|=i$ and $|J|=j$, there exists $g\in G$ such that $Ig\subseteq J$.…

We establish a combinatorial counterpart of the Cohen-Macaulay duality on a class of curve singularities which includes algebroid curves. For such singularities the value semigroup and the value semigroup ideals of all fractional ideals…

For a semisimple algebraic group $G$ of adjoint type with Lie algebra $\mathfrak g$ over the complex numbers, we establish a bijection between the set of closed orbits of the group $G \ltimes \mathfrak g^{\ast}$ acting on the variety of…

In this dissertation, we tackle the problem of describing the equations of the Rees algebra of I for I =(J,y), with J being of linear type. Throughout, such ideals are referred to as ideals of almost-linear type. In Theorem A, we give a…