相关论文: On Linear Difference Equations over Rings and Modu…

Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed. Two of them are new. There are a methods for computing adjoined matrices and solving system of linear equations in a commutative…

We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…

In this work we develop the theory of Gr\"obner bases for modules over the ring of univariate linearized polynomials with coefficients from a finite field.

Residue complexes were introduced by Grothendieck in algebraic geometry. These are canonical complexes of injective modules that enjoy remarkable functorial properties (traces). In this paper we study residue complexes over noncommutative…

We define pullback and separated presentations of modules over pullback rings, and, if the ring is a pullback of epimorphisms over a semisimple ring, an algorithm reducing such a presentation of a module to an $R$-diagram. The latter is the…

In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems…

We investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular $j$-invariants. By analyzing quadratic points on some modular curves, we show that all elliptic…

We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli…

These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming…

In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…

Solution methods for linear equation systems in a commutative ring are discussed. Four methods are compared, in the setting of several different rings: Dodgson's method [1], Bareiss's method [2] and two methods of the author - method by…

We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential…

In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…

We discuss representations of the projective line over a ring $R$ with 1 in a projective space over some (not necessarily commutative) field $K$. Such a representation is based upon a $(K,R)$-bimodule $U$. The points of the projective line…

The theory of standard bases in polynomial rings with coefficients in a ring R with respect to local orderings is developed. R is a commutative Noetherian ring with 1 and we assume that linear equations are solvable in R.

A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on…

This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular…

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…

We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…