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In this paper we obtain the Wedderburn-Artin decomposition of a semisimple group algebra associated to a direct product of finite groups. We also provide formulae for the number of all possible group codes, and their dimensions, that can be construct
Externí odkaz:
http://arxiv.org/abs/2412.09695
In this paper we explore which part of the ideal lattice of a general ring is parametrized by its Cuntz semigroup $\mathrm{S}(R)$ and its ambient semigroup $\Lambda(R)$. We identify these classes of ideals as the quasipure ideals (a generalization of
Externí odkaz:
http://arxiv.org/abs/2411.00507
Autor:
Cimprič, J.
We prove a new quaternionic and a new matrix nullstellensatz. We also show that both theories are intertwined.
Comment: 16 pages, submitted
Comment: 16 pages, submitted
Externí odkaz:
http://arxiv.org/abs/2409.17850
Autor:
Goswami, Amartya
The aim of this series of papers is to study $z$-ideals of semirings. In this article, we introduce some distinguished classes of $z$-ideals of semirings, which include $z$-prime, $z$-semiprime, $z$-irreducible, and $z$-strongly irreducible ideals an
Externí odkaz:
http://arxiv.org/abs/2410.09052
Autor:
Azarang, Alborz
Let $R$ be a maximal subring of a ring $T$, and $(R:T)$, $(R:T)_l$ and $(R:T)_r$ denote the greatest ideal, left ideal and right ideal of $T$ which are contained in $R$, respectively. It is shown that $(R:T)_l$ and $(R:T)_r$ are prime ideals of $R$ a
Externí odkaz:
http://arxiv.org/abs/2406.12890
Autor:
Bavula, V. V.
The class of $\D$-locally nilpotent algebras (introduced in the paper) is a wide generalization of the algebras of differential operators on commutative algebras. Examples includes all the rings $\CD (A)$ of differential operators on commutative alge
Externí odkaz:
http://arxiv.org/abs/2406.07569
In this paper, we study the uniform dimension and the associated prime ideals of induced modules over skew PBW extensions.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/2404.18698
In this paper, the quotient of a Leavitt path algebra of an arbitrary graph by an $I$-basic graded ideal, and the quotient of a Leavitt path algebra of a row-finite graph by an arbitrary graded ideal are considered. The result of the quotient of a Le
Externí odkaz:
http://arxiv.org/abs/2402.04155
Autor:
Lyubimtsev, Oleg, Tuganbaev, Askar
A ring $R$ with center $C$ is said to be centrally essential if the module $R_C$ is an essential extension of the module $C_C$. In this paper, we study properties of ideals of centrally essential rings, centrally essential quaternion algebras, and gr
Externí odkaz:
http://arxiv.org/abs/2401.12510
Autor:
Příhoda, Pavel
This paper is a continuation of a previous work by the author and G. Puninski where iterated intersections of powers of ideals were studied in rings of iterated differential polynomials. We present a method which can be used to show that for every pr
Externí odkaz:
http://arxiv.org/abs/2401.06562