On the Maximal Containments of Lower Central Series Ideals

Leibniz algebras whose solvable ideal is the maximal extension of the nilradical

The paper is devoted to the so-called complete Leibniz algebras. It is known that a Lie algebra with a complete ideal is split. We will prove that this result is valid for Leibniz algebras whose complete ideal is a solvable algebra such that the codimension of nilradical is equal to the number of generators of the nilradical.

Abelian subalgebras and ideals of maximal dimension in Zinbiel algebras

In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Zinbiel algebras. We study Zinbiel algebras containing maximal abelian subalgebras of codimension $1$ and supersolvable Zinbiel algebras in which such subalgebras have codimension $2$, and we also analyze the case of filiform Zinbiel algebras. We give examples to clarify some results, including listing the values for $α$ and $β$ for the low dimensional Zinbiel algebras over the complex field that have been classified.

Direct Products of Modules Whose Endomorphism Rings have at Most Two Maximal Ideals

Monogeny classes and epigeny classes have proved to be useful in the study of direct sums of uniserial modules and other classes of modules. In this paper, we show that they also turn out to be useful in the study of direct products.

Abelian subalgebras and ideals of maximal dimension in Leibniz algebras

In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Leibniz algebras. We study Leibniz algebras containing abelian subalgebras of codimension 1, solvable and supersolvable Leibniz algebras for codimensions 1 and 2, nilpotent Leibniz algebras in case of codimension 2 and we also analyze the case of k-abelian p-filiform Leibniz algebras. Throughout the paper, we also give examples to clarify some results and the need for restrictions on the underlying field.

部分单射幺半群上理想的极大子半群

The maximal subsemigroups of the ideals on a monoid of partial injections

该研究针对n元链上保序部分单射幺半群$POI_n$的子幺半群$IOF_n^{par}$，刻画其格林关系与理想，并明确各理想的极大子半群存在三种不同类型。

Maximal ideals in commutative Banach algebras

We show that each maximal ideal in a commutative Banach algebra has codimension 1.

关于一类自同态环至多有四个极大理想的扩张范畴

On a category of extensions whose endomorphism rings have at most four maximal ideals

该研究描述了A_R和C_R为单列模的短正合序列的自同态环，并探究了这些短正合序列在直和方面的行为，涉及自同态环至多含四个极大理想的扩张范畴。

Hurwitz多项式环中的素理想与极大理想

Prime and maximal ideals in Hurwitz polynomial rings

本文刻画了Hurwitz多项式环中R-不相交理想为素理想的条件，并研究了极大理想的存在性及其由最小次数多项式生成的判定方法。

Maximal T-spaces of the free associative algebra over a finite field

In earlier work, it was established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]_0, had infinitely many maximal T-spaces, but exactly two maximal $ideals (each of which is a maximal T-space). However, aside from these two T-ideals, no examples of maximal T-spaces of k[c]_0 have been identified. This paper presents, for each finite field k, an infinite sequence of proper T-spaces of k[x]_0 (no one of which is a T-ideal), each of finite codimension, and for each one, both a linear basis for the T-space itself and a linear basis for a complementa…

关于一类模链的范畴，其自同态环至多有$2n$个极大理想

On a category of chains of modules whose endomorphism rings have at most $2n$ maximal ideals

本文研究一类带固定子模链的右$R$-模构成的加法范畴，描述其自同态环性质并分析该范畴对象的直和行为。

A commutative Bezout domain in which every maximal ideal is principal is an elementary divisor ring

In this article we revisit a problem regarding Bezout domains, namely, whether every Bezout domain is an elementary divisor domain. We prove that a Bezout domain in which every maximal ideal is principal is an elementary divisor ring

Maximal ideals and representations of twisted forms of algebras

Given a central simple algebra $\mathfrak{g}$ and a Galois extension of base rings $S/R$, we show that the maximal ideals of twisted $S/R$-forms of the algebra of currents $\mathfrak{g}(R)$ are in natural bijection with the maximal ideals of $R$. When $\mathfrak{g}$ is a Lie algebra, we use this to give a complete classification of the finite-dimensional simple modules over twisted forms of $\mathfrak{g}(R)$.

特征2域上的有限对称群代数中的极大理想

Maximal ideals in the finitary symmetric group algebra in characteristic two

本文解决了特征2域上有限对称群代数极大理想分类的悬而未决问题，通过关联其素理想与高阶Verlinde范畴，借助研究一般线性群倾斜模的厚张量理想完成了该工作。

On abelian subalgebras and ideals of maximal dimension in supersolvable lie algebras

In this paper, the main objective is to compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional supersolvable Lie algebras. We characterise the maximal abelian subalgebras of solvable Lie algebras and study solvable Lie algebras containing an abelian subalgebra of codimension 2. Finally, we prove that nilpotent Lie algebras with an abelian subalgebra of codimension 3 contain an abelian ideal with the same dimension, provided that the characteristic of the underlying field is not two. Throughout the paper, we also give several examples to clarify some results.

Maximal ideal spaces of invariant function algebras on compact groups

The paper contains a description of the maximal ideal spaces (spectra) $\cM_A$ of bi-invariant function algebras $A$ on a compact group $G$. There are natural compatible structures in $\cM_A$: it is a compact topological semigroup with involution, polar decomposition, and analytic structure. The paper contains a description of $\cM_A$ and related results on function algebras; for example, a bi-invariant function algebra on a connected compact Lie group is antisymmetric if and only if the Haar measure of its maximal torus is multiplicative on it. Some results are extended to the case of compact…

Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization)

We study the asymptotics at zero of continuous functions on (0, 1] by means of their asymptotic ideals, i.e., ideals in the ring of continuous functions on (0, 1] satisfying a polynomial growth condition at 0 modulo rapidly decreasing functions at 0. As our main result, we characterize maximal and prime ideals in terms of maximal and prime filters.