环与代数
We introduce the concepts of generalized compatible and cocompatible bimodules in order to characterize Gorenstein projective, injective and flat modules over trivial ring extensions. Let $R\ltimes M$ be a trivial extension of a ring $R$ by…
In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…
We characterize all real matrix semigroups satisfying a mild boundedness assumption, without assuming continuity. Besides the continuous solutions of the semigroup functional equation, we give a description of solutions arising from…
In this paper, we introduce the notion of pseudo-triangular norm (pseudo-t-norm, for short) as a classes of weakly associative operations on trellises and as a generalization of triangular norm (t-norm, for short) on bounded trellises and…
I present a universal method, called pivotal condensation, for calculating stoichiometric factors of chemical reactions. It can be done by hand, even for rather complicated reactions. The main trick, which I call kernel pivotal condensation…
In the present paper automorphisms, local and 2-local automorphisms of $n$-dimensional null-filiform and filiform associative algebras are studied. Namely, a common form of the matrix of automorphisms and local automorphisms of these…
A multiplicative hyperring is a well-known type of algebraic hyperstructures which extend a ring to a structure in which the addition is an operation but multiplication is a hyperoperation. Let G be a commutative multiplicative hyperring…
In this thesis, we investigated some properties of (left)near fields and derived some results. We are focusing on $D(\alpha, \beta)$ which is the generalized set of distributive elements of a nearfield. In particular, we investigated some…
We give here a review of results about double bialgebras, that is to say bialgebras with two coproducts, the first one being a comodule morphism for the coaction induced by the second one. An accent is put on the case of connected…
In the present paper, we prove that a local derivation on the octonion (Cayley) algebra $\mathbb{O}$ over an arbitrary field, satisfying some conditions is a derivation, and every 2-local derivation on $\mathbb{O}$ is a Jordan derivation.
This manuscript proposes a generalized inverse for a dual matrix called dual Drazin generalized inverse (DDGI) which generalizes the notion of the dual group generalized inverse (DGGI). Under certain necessary and sufficient conditions, we…
As it is known, the defining identities of a free Novikov algebra can be obtained from a commutative algebra with a derivation. In this paper, we consider a class of algebras obtained from the class of associative algebras with a derivation…
We present the generalized Drazin inverse for certain anti-triangular operator matrices. Let $E,F,EF^{\pi}\in \mathcal{B}(X)^d$. If $EFEF^{\pi}=0$ and $F^2EF^{\pi}=0$, we prove that $M=\left( \begin{array}{cc} E&I F&0 \end{array} \right)$…
We introduce the variety ${\mathfrak B}_{\textrm{sup}}$ of bicommutative superalgebras over an arbitrary field of characteristic different from 2. The variety consists of all nonassociative ${\mathbb Z}_2$-graded algebras satisfying the…
We prove a version of a theorem of Auslander for finite group actions or coactions on noetherian polynomial identity Artin-Schelter regular algebra.
Modern advances in general-purpose computer algebra systems offer solutions to a variety of problems, which in the past required substantial time investments by trained mathematicians. An excellent example of such development are the…
Closed form expressions for a logarithm of general multivector (MV) in base-free form in real geometric algebras (GAs) Cl(p,q) are presented for all n=p+q=3. In contrast to logarithm of complex numbers (isomorphic to Cl(0,1), 3D logarithmic…
We introduce the concept of braided noncommutative Poisson bialgebras. The theory of cocycle bicrossproducts for noncommutative Poisson bialgebras is developed. As an application, we solve the extending problem by using some non-abelian…
We develop basic homological machinery for Z-algebras in order to prove a version of local duality for Ext-finite connected Z-algebras. As an application, we compare two notions of regularity for such algebras.
We introduce a generalization of the universal valuation semiring defined by Jeffrey and Noah Giansiracusa. We then explicitly characterize the additive structure of this semiring and show that, when applied to $\mathbb Q$, this…