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The rank of a commutative semigroup

Antonio M. Cegarra, Mario Petrich (2009)

Mathematica Bohemica

The concept of rank of a commutative cancellative semigroup is extended to all commutative semigroups S by defining rank S as the supremum of cardinalities of finite independent subsets of S . Representing such a semigroup S as a semilattice Y of (archimedean) components S α , we prove that rank S is the supremum of ranks of various S α . Representing a commutative separative semigroup S as a semilattice of its (cancellative) archimedean components, the main result of the paper provides several characterizations...

The semantical hyperunification problem

Klaus Denecke, Jörg Koppitz, Shelly Wismath (2001)

Discussiones Mathematicae - General Algebra and Applications

A hypersubstitution of a fixed type τ maps n-ary operation symbols of the type to n-ary terms of the type. Such a mapping induces a unique mapping defined on the set of all terms of type t. The kernel of this induced mapping is called the kernel of the hypersubstitution, and it is a fully invariant congruence relation on the (absolutely free) term algebra F τ ( X ) of the considered type ([2]). If V is a variety of type τ, we consider the composition of the natural homomorphism with the mapping induced...

The set of minimal distances in Krull monoids

Alfred Geroldinger, Qinghai Zhong (2016)

Acta Arithmetica

Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say a = u 1 · . . . · u k . The set (a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ maxexp(G)-2,(G)-1 and that equality holds if every...

Currently displaying 2181 – 2200 of 2557