Tensor products of idempotent semimodules. An algebraic approach

This is a study of universal problems for semimodules, in particular coequalizers, coproducts, and tensor products. Furthermore the structure theory of semiideals of the semiring of natural numbers is extended.

The aim of this work is to prove that the Riesz tensor product of two archimedean $d$-algebras is itself a $d$-algebra.

In this paper we solve a problem, originally raised by Grothendieck, on the transfer of Cohen-Macaulayness to tensor products of algebras over a field. As a prelude to this, we investigate the grade for some specific types of ideals that play a primordial role within the ideal structure of such constructions.

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The aim of this paper is to introduce the notion of fully S-idempotent modules as a generalization of fully idempotent modules and investigate some properties of this class of modules.

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

For $ C^*$-algebras $ \mathfrak{A}, A$ and $ B $ where $ A $ and $ B $ are $ \mathfrak{A} $-bimodules with compatible actions, we consider amalgamated $ \mathfrak{A} $-module tensor product of $ A $ and $ B $ and study its relation with the C*-tensor product of $A$ and $B$ for the min and max norms. We introduce and study the notions of module tensorizing maps, module exactness, and module nuclear pairs of $ C^*$-algebras in this setting. We give concrete examples of $C^*$-al...

In this work we discuss an elementary self-contained presentation of the notion of a semiabelian category, introduced by Raikov and Palamodov. Fundamental examples of (non-abelian) semiabelian categories occuring in Functional Analysis and Topological Algebra are treated in detail throughout the paper.

We develop the duality theory between ideals of multilinear operators and tensor norms that arises from the geometric approach of $\Sigma$-operators. To this end, we introduce and develop the notions of $\Sigma$-ideals of multilinear operators and $\Sigma$-tensor norms. We establish the foundations of this theory by proving a representation theorem for maximal $\Sigma$-ideals of multilinear operators by finitely generated $\Sigma$-tensor norms and a duality theorem for $\Sigm...

In this study we give an answer to the open question about the Riesz tensor product of ideals and bands of a Riesz space. We prove among other results that the Dedekind completion of the Riesz tensor product of two ideals is again an ideal.

For $C^*$-algebras $A$ and $B$, we prove the slice map conjecture for ideals in the operator space projective tensor product $A \hat\otimes B$. As an application, a characterization of prime ideals in the Banach $\ast$-algebra $A\hat\otimes B$ is obtained. Further, we study the primitive ideals, modular ideals and the maximal modular ideals of $A\hat\otimes B$. It is also shown that the Banach $\ast$-algebra $A\hat\otimes B$ possesses Wiener property; and that, for a subhomog...