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- Author or Editor: Kalle Kaarli x
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If A is a minimal algebra (that is, has no proper subalgebras) then the set S 2(A) of all subalgebras of A 2 has a natural structure of ordered involutive monoid. This paper gives a characterization of monoids S that appear in the role of this monoid if A is finite, weakly diagonal (every subalgebra of A 2 contains the graph of an automorphism of A) and has a majority term.
This paper gives a complete characterization, up to categorical equivalence, and up to term equivalence, of finite algebras that have no proper subalgebras, have no isomorphic quotients, and generate arithmetical varieties.
This paper gives a classification of arithmetical affine complete varieties of finite type up to categorical equivalence. It is proved that two such varieties are equivalent as categories if and only if their weakly diagonal generators have isomorphic monoids of bicongruences. Moreover, it is proved that the monoids appearing in this situation are precisely the inverse factorizable monoids with zero, with distributive lattice of idempotents, and satisfying a certain idempotent-unit condition (IU).
Abstract
This paper gives a complete description of the behaviour of torsion-free abelian groups of rank 3 with respect to endoprimality.
