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Relations on a lattice of varieties of completely regular semigroups

Mario Petrich (2020)

Mathematica Bohemica

Completely regular semigroups 𝒞ℛ are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes 𝒞ℛ a variety; its lattice of subvarieties is denoted by ( 𝒞ℛ ) . We study here the relations 𝐊 , T , L and 𝐂 relative to a sublattice Ψ of ( 𝒞ℛ ) constructed in a previous publication. For 𝐑 being any of these relations, we determine the 𝐑 -classes of all varieties in the lattice Ψ as well as the restrictions of 𝐑 to Ψ .

Relative block semigroups and their arithmetical applications

Franz Halter-Koch (1992)

Commentationes Mathematicae Universitatis Carolinae

We introduce relative block semigroups as an appropriate tool for the study of certain phenomena of non-unique factorizations in residue classes. Thereby the main interest lies in rings of integers of algebraic number fields, where certain asymptotic results are obtained.

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