Related papers: An additional structure over integer rings $\mathb…

We settle a long-standing problem in the theory of Hecke algebras of complex reflection groups by constructing many (graded) integral cellular bases of these algebras. As applications, we explicitly construct the simple modules of Ariki's…

This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…

Let R be a ring and G a group. An R-module A is said to be artinian-by-(finite rank) if TorR(A) is artinian and A/TorR(A) has finite R-rank. The authors study ZG-modules A such that A/CA(H) is artinian-by-(finite rank) (as a Z-module) for…

We give a necessary and sufficient condition for a type of generalized power series to be algebraic over the ring of power series with coefficients in a finite field. This result extend a classical theorem of Huang-Stefanescu.

We characterize symbolic powers of prime ideals in polynomial rings over any field in terms of $\mathbb{Z}$-linear differential operators, and of prime ideals in polynomial rings over complete discrete valuation rings with a $p$-derivation…

Birack modules are modules over an algebra Z[X] associated to a finite birack X. In previous work, birack module structures on Z mod n were used to enhance the birack counting invariant. In this paper, we use birack modules over Laurent…

In this article we prove various results about transferring or lifting $\mathrm{A}_\infty$-algebra structures along quasi-isomorphisms over a commutative ring.

We found a regularity of the behavior of primes that allows to represent both prime and natural numbers as infinite matrices with a common formation rule of their rows. This regularity determines a new class of infinite cyclic groups that…

We study symplectic linear algebra over the ring $\Rt$ of Colombeau generalized numbers. Due to the algebraic properties of $\Rt$ it is possible to preserve a number of central results of classical symplectic linear algebra. In particular,…

This extended abstract gives a construction for lifting a Gr\"obner basis algorithm for an ideal in a polynomial ring over a commutative ring R under the condition that R also admits a Gr\"obner basis for every ideal in R.

We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…

In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring $\cR$, we prove…

We give a necessary condition for algebraicity of finite modules over the ring of formal power series. This condition is given in terms of local zero estimates. In fact we show that this condition is also sufficient when the module is a…

We investigate generalized quadratic forms with values in the set of rational integers over quadratic fields. We characterize the real quadratic fields which admit a positive definite binary generalized form of this type representing every…

Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…

In this paper, we consider some structures of linear codes over the ring $\mathcal{R}_k=R[v_1,\dots,v_k],$ where $v_i^2=v_i$ forall $i=1,\dots,k),$ and $R$ is a finite commutative Frobenius ring.

Hyperfields and systems are two algebraic frameworks which have been developed to provide a unified approach to classical and tropical structures. All hyperfields, and more generally hyperrings, can be represented by systems. Conversely, we…

In this paper, we define a certain Hodge-theoretic structure for an arbitrary variety X over the complex number field by using the theory of mixed Hodge module due to Morihiko Saito. We call it an arithmetic Hodge structure of X. It is…

This article investigates the splitting problem for finitely generated projective modules $P$ over affine algebras over algebraically closed fields and their polynomial extensions. We then address an open question due to M. Roitman on monic…

We introduce the Picard group of corings. We extend the well-known exact sequence from algebras and coalgebras over fields to corings. We extend the Aut-Pic property to corings and we give some new examples of corings having this property.…