Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

This paper surveys and develops links between polynomial invariants of finite groups,
factorization theory of Krull domains, and product-one sequences over finite groups. The …

This is a survey on factorization theory. We discuss finitely generated monoids (including
affine monoids), primary monoids (including numerical monoids), power sets with set …

Oftentimes the elements of a ring or semigroup can be written as finite products of
irreducible elements. An element a can be a product of k irreducibles and a product of l …

It has been recently observed that fundamental aspects of the classical theory of
factorization can be greatly generalized by combining the languages of monoids and …

It is well known that the ring of integers of an algebraic number field may fail to have unique
factorization. In the development of algebraic number theory in the 19th century, this failure …

We investigate the Jordan-Hölder property (JHP) in exact categories. First, we show that
(JHP) holds in an exact category if and only if the Grothendieck monoid introduced by …

Let R be an associative ring. This monograph deals with the right R-modules MR whose
endomorphism ring End (MR) is semilocal. More generally, let A be any preadditive …

Let H be a commutative semigroup with unit element such that every non-unit can be written
as a finite product of irreducible elements (atoms). For every k∈ ℕ, let 𝒰 k (H) denote the set …

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 …