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This paper is primarily concerned with studying finite-dimensional anti-commutative nonassociative algebras in which every centralizer is an ideal. These are shown to be anti-associative and are classified over a general field $F$; in…

We construct a nil algebra over a countable field which has finite but non-zero Gelfand-Kirillov dimension.

In this work the classification of filiform Leibniz superalgebras of nilindex $n+m,$ where $n$ and $m$ ($m \ne 0$) are dimensions of even and odd parts, respectively, is obtained.

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

In this work nul-filiform and filiform Zinbiel algebras are described up to isomorphism. Moreover, the classification of complex Zinbiel algebras is extended from dimensions $\leq 3$ up to the dimension $4.$

In this paper we give the complete classification of $5$-dimensional complex solvable symmetric Leibniz algebras.

We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.

We investigate the class groups and the distribution of prime divisors in affine monoid algebras over fields and thereby extend the result of Kainrath that every finitely generated integral algebra of Krull dimension at least 2 over an…

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.

A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. We prove that a quadratic…

In this paper we find exact formulas for the numbers of partitions and compositions of an element into $m$ parts over a finite field, i.e. we find the number of nonzero solutions of the equation $x_1+x_2+...+x_m=z$ over a finite field when…

This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically…

We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},\ldots , a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$, where…

We generalize Amitsur's construction of central simple algebras over a field $F$ which are split by field extensions possessing a derivation with field of constants $F$ to nonassociative algebras: for every central division algebra $D$ over…

We prove that two infinite p-adic semi-algebraic sets are isomorphic (i.e. there exists a semi-algebraic bijection between them) if and only if they have the same dimension.

An algebra is said to be \emph{$\tau$-tilting finite} provided it has only a finite number of $\tau$-rigid objects up to isomorphism. We associate a category to each such algebra. The objects are the wide subcategories of its category of…

We investigate objects in symmetric tensor categories that have simultaneously finite symmetric and finite exterior algebra. This forces the characteristic of the base field to be $p>0$, and the maximal degree of non-vanishing symmetric and…

All quasi-affine connected Generalized Dynkin Diagram with rank $= 5$ are found. All quasi-affine Nichols (Lie braided) algebras with rank $ 5$ are also found.