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 …

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 …

Transfer Krull monoids are a recently introduced class of monoids and include the
multiplicative monoids of all commutative Krull domains as well as of wide classes of non …

If H is a monoid and a= u1··· uk∈ H with atoms (irreducible elements) u1,…, uk, then k is a
length of a, the set of lengths of a is denoted by Ⅼ (a), and ℒ (H)={Ⅼ (a)| a∈ H} is the system …

A submonoid S of a given monoid H is called monadic if it is a divisor-closed submonoid of
H generated by one element (ie, there is some (non-zero) b∈ H such that S is the smallest …

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 …

Let H be an atomic monoid. The set of distances Δ (H) of H is the set of all d∈ N with the
following property: there are irreducible elements u 1,…, uk, v 1…, v k+ d such that u 1⋅…⋅ …

Let R be a ring and let be a small class of right R-modules which is closed under finite direct
sums, direct summands, and isomorphisms. Let denote a set of representatives of …

Let H be a Krull monoid with class group G and suppose that each class contains a prime
divisor. Then every element a∈ H has a factorization into irreducible elements, and the set L …

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