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Bases for certain varieties of completely regular semigroups

Mario Petrich (2021)

Commentationes Mathematicae Universitatis Carolinae

Completely regular semigroups equipped with the unary operation of inversion within their maximal subgroups form a variety, denoted by 𝒞ℛ . The lattice of subvarieties of 𝒞ℛ is denoted by ( 𝒞ℛ ) . For each variety in an -subsemilattice Γ of ( 𝒞ℛ ) , we construct at least one basis of identities, and for some important varieties, several. We single out certain remarkable types of bases of general interest. As an application for the local relation L , we construct 𝐋 -classes of all varieties in Γ . Two figures illustrate...

Bases of minimal elements of some partially ordered free abelian groups

Pavel Příhoda (2003)

Commentationes Mathematicae Universitatis Carolinae

In the present paper, we will show that the set of minimal elements of a full affine semigroup A 0 k contains a free basis of the group generated by A in k . This will be applied to the study of the group K 0 ( R ) for a semilocal ring R .

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