Related papers: A semigroup-theoretical view of direct-sum decompo…

In this paper we develop an ideal structure theory for the class of left reductive regular semigroups and apply it to several subclasses of popular interest. In these classes we observe that the right ideal structure of the semigroup is…

We give an elementary characterization of those (abelian) semigroups $M$ that are direct limits of countable sequences of finite direct products of monoids of the form $C\cup\{0\}$ for monogenic groups $C$. This characterization involves…

In this paper we develop a new groupoid-based structure theory for the class of regular $*$-semigroups. This class occupies something of a `sweet spot' between the important classes of inverse and regular semigroups, and contains many…

Let $C$ be a coalgebra. We investigate the problem of when the rational part of every finitely generated $C^*$-module $M$ is a direct summand $M$. We show that such a coalgebra must have at most countable dimension, $C$ must be artinian as…

Let $R$ be a commutative ring and $\Gamma$ be an infinite discrete group. The algebraic $K$-theory of the group ring $R[\Gamma]$ is an important object of computation in geometric topology and number theory. When the group ring is…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called $absolutely$ $\mathcal C$-$closed$ if for any homomorphism $h:X\to Y$ to a topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. Let…

We introduce an axiomatization of the notion of a semidirect product of locally compact quantum groups and study properties. Our approach is slightly different from the one introduced in the thesis of S.~Roy and, unlike the investigations…

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero…

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…

This paper is devoted to the study of the endo-structure of infinite direct sums $\bigoplus_{i \in I} M_i$ of indecomposable modules $M_i$ over a ring $R$. It is centered on the following question: If $S = \text{End}_R \bigl( \bigoplus_{i…

A completely simple semigroup S is a semigroup without zero which has no proper ideals and contains a primitive idempotent. It is known that S is a regular semigroup and any completely simple semigroup is isomorphic to the Rees matrix…

Let $\mathbf{G}$ be either a simple linear algebraic group over an algebraically closed field of positive characteristic or a quantum group at a root of unity. We define new classes of indecomposable $\mathbf{G}$-modules, which we call…

A rational function on a real algebraic curve $C$ is called separating if it takes real values only at real points. Such a function defines a covering $\mathbb R C\to\mathbb{RP}^1$. Let $c_1,\dots,c_r$ be connected components of $\mathbb R…

In this paper we study (non-commutative) rings $R$ over which every finitely generated left module is a direct sum of cyclic modules (called left FGC-rings). The commutative case was a well-known problem studied and solved in 1970s by…

A two-dimensional chiral conformal field theory can be viewed mathematically as the representation theory of its chiral algebra, a vertex operator algebra. Vertex operator algebras are especially well suited for studying logarithmic…

In this paper subcentral (resp., central) idempotent series and composition subcentral (resp., central) idempotent series in an inverse semigroup are introduced and investigated. It is shown that if $S=EG$ is a factorizable inverse monoids…

We initiate the study of the internal structure of C*-algebras associated to a left cancellative semigroup in which any two principal right ideals are either disjoint or intersect in another principal right ideal; these are variously called…

Let $(\mathfrak{C},\mathbb{E},\mathfrak{s})$ be an Ext-finite, Krull-Schmidt and $k$-linear extriangulated category with $k$ a commutative artinian ring. We define an additive subcategory $\mathfrak{C}_r$ (respectively, $\mathfrak{C}_l$) of…

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.

It is proved that, for a left hereditary ring, an arbitrary left module has a representation in the form of the direct sum of a stable left module and indecomposable projective left modules (if and only if an arbitrary left module has a…