环与代数
A graph of Gelfand-Kirillov dimension three is a connected finite essential graph such that its Leavitt path algebra has Gelfand-Kirillov dimension three. We provide number-theoretic criteria for graphs of Gelfand-Kirillov dimension three…
This article explores the structure theory of compatible generalized derivations of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $\omega$-Lie algebra can be embedded…
The aim of this article is to advance the knowledge on the theory of skew left braces. We introduce a subclass of skew left braces, which we denote by $\mathcal{I}_n$, $n \ge 1$, such that elements of the annihilator and lower central…
We study unital commutative associative algebras and their associated n-Lie algebras, showing that they are strong transposed Poisson n-Lie algebras under specific compatibility conditions. Furthermore, we generalize the simplicity…
We study simple Lie algebras generated by extremal elements, over arbitrary fields of arbitrary characteristic. We show: (1) If the extremal geometry contains lines, then the Lie algebra admits a $5 \times 5$-grading that can be…
The present article is devoted to studying the categorical relationships between the categories of Hopf trusses, weak twisted post-Hopf algebras, introduced by Wang (2023), and weak twisted relative Rota-Baxter operators. The latter objects…
A ring $R$ is called left strictly $(<\aleph_{\alpha})$-noetherian if $\aleph_{\alpha}$ is the minimum cardinal such that every ideal of $R$ is $(<\aleph_{\alpha})$-generated. In this note, we show that for every singular (resp., regular)…
In this paper the 3-hypergraph semigroups and 3-hypergraph semirings from 3-hypergraphs $\mathbb{H}$ are introduced and the varieties generated by them are studied. It is shown that all 3-hypergraph semirings $S_{\scriptscriptstyle…
A quadratic Novikov algebra is a Novikov algebra $(A, \circ)$ with a symmetric and nondegenerate bilinear form $B(\cdot,\cdot)$ satisfying $B(a\circ b, c)=-B(b, a\circ c+c\circ a)$ for all $a$, $b$, $c\in A$. This notion appeared in the…
The class of strictly sign regular (SSR) matrices has been extensively studied by many authors over the past century, notably by Schoenberg, Motzkin, Gantmacher, and Krein. A classical result of Gantmacher-Krein assures the existence of SSR…
Let F be a field. We investigate the greatest possible dimension t_n(F) for a vector space of n-by-n matrices with entries in F and in which every element is triangularizable over the ground field F. It is obvious that t_n(F) is greater…
In this paper, we introduce the category of brace triples in a braided monoidal setting and prove that it is isomorphic to the category of s-Hopf braces, which are a generalization of cocommutative Hopf braces. After that, we obtain a…
Global representation rings were discovered by Sarah Witherspoon in 1995 and the Knutson Index was introduced by the second author in 2022. In the present paper we introduce the Knutson Index for general commutative rings and study it for…
Kronecker's 1856 paper contains a solvability theorem that is useful to construct unsolvable algebraic equations. We show how Kronecker's solvability theorem can be derived naturally via a polynomial complete decomposition method. This…
The purpose of this paper is to introduce a new family of semigroups - the free projection-generated regular $*$-semigroups - and initiate their systematic study. Such a semigroup $PG(P)$ is constructed from a projection algebra $P$, using…
MV-monoids are algebras $\langle A,\vee,\wedge, \oplus,\odot, 0,1\rangle$ where $\langle A, \vee, \wedge, 0, 1\rangle$ is a bounded distributive lattice, both $\langle A, \oplus, 0 \rangle$ and $\langle A, \odot, 1\rangle$ are commutative…
Skew bracoids have been shown to have applications in Hopf-Galois theory. We show that a certain family of skew bracoids correspond bijectively with left cancellative semibraces. A consequence of this correspondence is that skew bracoids in…
We know that coalgebra measurings behave like generalized maps between algebras. In this note, we show that coalgebra measurings between commutative algebras induce morphisms between higher order Hochschild homology groups of algebras. By…
In this paper we prove the following theorem. Let R be a prime Noetherian ring with krull dimension |R| = n where n is a positive integer. Let Q be the Goldie quotient ring of R. For a fixed positive integer m < n, let xm be the set of all…
The problem of extending derivations of a field $F$ to an $F-$algebra $B$ is widely studied in commutative algebra and non-commutative ring theory. For example, every derivation of $F$ extends to $B$ if $B$ is a separable algebraic…