Related papers: Ideals in the Goldman Algebra
In this article we investigate when a homogeneous ideal in a graded ring is normal, that is, when all positive powers of the ideal are integrally closed. We are particularly interested in homogeneous ideals in an N-graded ring generated by…
The aim of this note is to understand under which conditions invertible modules over a commutative S-algebra in the sense of Elmendorf, Kriz, Mandell and May give rise to elements in the algebraic Picard group of invertible graded modules…
In this paper, we introduce the concept of fuzzy Hom-Lie subalgebras (ideals) of Hom-Lie algebras and we investigate some of their properties. We study the relationship between fuzzy Hom-Lie subalgebras (resp. ideals) and Hom-Lie…
We propose a general quantum Hamiltonian formalism of a renormalization group (RG) flow with an emphasis on generalized symmetry by interpreting the elementary relationship between homomorphism, quotient ring, and projection. In our…
The purpose of this work is to extend the study of the commutative rings whose lattice of ideals can be a structure of BL-algebra as carry out by Heubo et al in 2018, to non commutative rings appointed in the work as pseudo BL-rings. We…
In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…
Let $R$ be a Noetherian ring, $I$ and $J$ two ideals of $R$ and $t$ an integer. Let $S$ be the class of Artinian $R$-modules, or the class of all $R$-modules $N$ with $\dim_RN\leq k$, where $k$ is an integer. It is proved that $\inf\{i:…
We introduce to the context of multigraded modules the methods of modules over categories from algebraic topology and homotopy theory. We develop the basic theory quite generally, with a view toward future applications to a wide class of…
Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups,…
We approach a problem of realising algebraic objects in a certain universal equivariant stable homotopy theory; the global homotopy theory of Schwede. Specifically, for a global ring spectrum $R$, we consider which classes of ring…
In this paper we have discussed the ideals in Abel Grassmann's groupoids and construct their topologies.
We show that a compact complex parallelisable nilmanifold has unobstructed deformations if and only if its associated Lie algebra satisfies a reality condition and is a free Lie algebra in a variety of Lie algebras, that is, defined by a…
Let $R$ be a commutative ring with identity and $S$ a multiplicatively closed subset of $R$. This paper aims to introduce the concept of $S$-$n$-ideals as a generalization of $n$-ideals. An ideal $I$ of $R$ disjoint with $S$ is called an…
In the article "Non-commutative Grobner bases for commutative algebras", Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and initial ideals of those ideals in the free associative algebra which contain the…
We investigate certain ideals (associated with Blaschke products) of the analytic Lipschitz algebra $A^\alpha$, with $\alpha>1$, that fail to be "ideal spaces". The latter means that the ideals in question are not describable by any size…
We continue the study of r-ideals, l-ideals, and HSA's in operator algebras. Some applications are made to the structure of operator algebras, including Wedderburn type theorems for a class of operator algebras. We also consider the…
P. Aluffi introduced in [1] a new graded algebra in order to conveniently express characteristic cycles in the theory of singular varieties. This algebra is attached to a surjective ring homomorphism $A\surjects B$ by taking a suitable…
This article takes up the challenge of extending the classical Real Nullstellensatz of Dubois and Risler to left ideals in a *-algebra A. After introducing the notions of non-commutative zero sets and real ideals, we develop three themes…
Given an arbitrary graph E and any field K, a new class of simple left modules over the Leavitt path algebra L of the graph E over K is constructed by using vertices that emit infinitely many edges. The corresponding annihilating primitive…
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…