We examine the pointed protomodular category SKB of left skew braces. We study the
notion of commutator of ideals in a left skew brace. Notice that in the literature,“product” of …

We combine the language of monoids with the language of preorders so as to refine some
fundamental aspects of the classical theory of factorization and prove an abstract …

Abstract Extending the Wedderburn–Artin theory of (classically) semisimple associative
rings to the realm of topological rings with right linear topology, we show that the abelian …

The category k-BFAlg of all k-algebras with a bilinear form, whose objects are all pairs (R, b)
where R is a k-algebra and b: R× R→ k is a bilinear mapping, is equivalent to the category of …

A module over a ring R is pure projective provided it is isomorphic to a direct summand of a
direct sum of finitely presented modules. We develop tools for the classification of pure …

We show that every finitely generated conical refinement monoid can be represented as the
monoid\mathcal V (R) V (R) of isomorphism classes of finitely generated projective modules …

We study direct-sum decompositions of torsion-free, finitely generated modules over a
(commutative) Bass ring R through the factorization theory of the corresponding monoid T …

Industry 4.0 affects all components of the modern industry value chain. The accelerating use
of the Internet and the convergence of industrial and operational networks constantly …

In this paper, we study the behavior of endomorphism rings of indecomposable (uniform)
quasi-injective modules. A very natural question here is, for a morphism f: A→ B, with A, B …

In this paper, we introduce the notion of G-liftable ideals, which extends the liftable ideas
defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the …