环与代数
Let $A=\mathcal{A}(E,\sigma)$ be a $3$-dimensional quantum polynomial algebra where $E$ is $\mathbb{P}^{2}$ or a cubic divisor in $\mathbb{P}^{2}$, and $\sigma\in \mathrm{Aut}_{k}E$. Artin-Tate-Van den Bergh proved that $A$ is finite over…
In a 2121 paper with G\'abor Cz\'edli, we introduced and verified the Three-pendant Three-crown Property, 3P3C, for congruence lattices of slim, planar, semimodular lattices. The proof is very long; in part, because it relies on Cz\'edli's…
The Fagundes-Mello conjecture asserts that every multilinear polynomial on upper triangular matrix algebras is a vector space, which is an improtant variation of the old and famous Lvov-Kaplansky conjecture. The goal of the paper is to give…
We introduce partial representation of a finite groupoid $G$ on an algebra $A$ and show that the partial groupoid representations of $G$ are in one-to-one correspondence with the representations of the algebra generated by the Birget-Rhodes…
In order to study certain algebraic objects, and notably algebraic groups, Serre introduced the notion on invariants, in particular cohomological invariants. The construction of non-trivial cohomological invariants of algebraic groups is an…
In a recent paper, Matthew Baker and Oliver Lorscheid showed that Descartes's Rule of Signs and Newton's Polygon Rule can both be interpreted as multiplicities of polynomials over hyperfields. Hyperfields are a generalization of fields…
This paper describes the centers of the universal enveloping algebras and the invariant rings of the standard filiform Lie algebras over fields of characteristic zero and also over large enough prime characteristic. We determine explicit…
Given a collection $\{ G_i\}_{i=1}^d$ of finite groups and a ring $R$, we define a subring of the ring $M_n(R)$ ($n = \sum_{i=1}^d|G_i|)$ that encompasses all the individual group rings $R[G_i]$ along the diagonal blocks as $G_i$-circulant…
A Rota-Baxter Lie algebra $\mathfrak{g}_T$ is a Lie algebra $\mathfrak{g}$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie algebra…
We devise a condition strictly between the existence of an $n$-ary and an $n{+}1$-ary near-unanimity term. We evaluate exactly the distributivity and modularity levels implied by such a condition.
Although there is no natural internal product for hermitian forms over an algebra with involution of the first kind, we describe how to multiply two $\varepsilon$-hermitian forms to obtain a quadratic form over the base field. This allows…
An averaging operator on an associative algebra $A$ is an algebraic abstraction of the time average operator on the space of real-valued functions defined in time-space. In this paper, we consider relative averaging operators on a bimodule…
Given a Galois extension $R^{\beta} \subset R$, where $\beta$ is an action of a finite groupoid on a noncommutative ring, we present some conditions to the Galois map be injective.
This article presents a generalization of the RSA cryptosystem for rings with commuting ideals. An analogue of the Euler function for ideals and the concept of an RSA-ideal are defined. An analog of a cryptosystem for the ring with…
We show that there is a one-to-one correspondence between the partial actions of a groupoid $G$ on a set $X$ and the inverse semigroupoid actions of the Exel's inverse semigroupoid $S(G)$ on $X$. We also define inverse semigroupoid…
For a ring $A$, we consider the question whether every bounded above cochain complex of injective $A$-modules which is acyclic is null-homotopic. We show that if $A$ is left and right noetherian and has a dualizing complex, then this…
The double extension and the T*-extension are classical methods for constructing finite dimensional quadratic Lie algebras. The first one gives an inductive classification in characteristic zero, while the latest produces quadratic…
All algebras of a certain type are said to form a Nielsen-Schreier variety if every subalgebra of a free algebra is free. This property has been perceived as extremely rare; in particular, only six Nielsen-Schreier varieties of algebras…
In this paper, we introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology. Consequently, we use this cohomology to characterize…
Quite much recent studies has been attracted to the operated algebra since it unifies various notions such as the differential algebra and the Rota-Baxter algebra. An $\Omega$-operated algebra is a an (associative) algebra equipped with a…