Related papers: Remarks on Semimodules
We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not…
We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and…
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are…
We revisit the notion of flatness for semimodules over semirings. In particular, we introduce and study a new notion of uniformly flat semimodules based on the exactness of the tensor functor. We also investigate the relations between this…
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…
We modify the well-known tensor product of modules over a semiring, in order to treat modules over hyperrings, and, more generally, for bimodules (and bimagmas) over monoids. The tensor product of residue hypermodules is functorial. Special…
We investigate some general machinery for describing semidualizing modules over generic constructions like ladder determinantal rings with coefficients in a normal domain. We also pose and investigate natural localization questions that…
Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and…
This thesis is dedicated to developing a dilation theory for semigroups of completely positive maps. The first part treats two-parameter semigroups, and contains also contributions to dilation theory of product system representations. The…
In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the…
Let $R$ be a commutative ring with identity and $M$ a unitary $R$-module. The purpose of this paper is to introduce the concept of semi-$n$-submodules as an extension of semi $n$-ideals and $n$-submodules. A proper submodule $N$ of $M$ is…
The main purpose of this paper is to investigate prime, primary, and maximal ideals of semirings. The localization and primary decomposition of ideals in semirings are also studied.
Let $S$ be a semiring. An $S$-semimodule $M$ is called a multiplication semimodule if for each subsemimodule $N$ of $M$ there exists an ideal $I$ of $S$ such that $N=IM$. In this paper we investigate some properties of multiplication…
Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no non-zero injective semimodules (e.g. the semiring of non-negative integers). In this…
In this paper, we introduce homological structure theory of semirings and CP-semirings---semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, subtractive, and anti-bounded, CP-semirings. We…
In this paper, we introduce and investigate \emph{semicorings} over associative semirings and their categories of \emph{semicomodules.} Our results generalize old and recent results on corings over rings and their categories of comodules.…
In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra,…
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…
We give an introduction to the concept of Kan extensions, and study its relation with the notions of coend and adjoint functors. We state and prove in detail a well known formula to compute Kan extensions by using coends: a certain colimit…
We study the existence of nontrivial semidualizing DG modules over tensor products of DG algebras over a field. In particular, this gives a lower bound on the number of semidualizing DG modules over the tensor product.