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Adjoint regular rings.

Heatherly, Henry E., Tucci, Ralph P. (2002)

International Journal of Mathematics and Mathematical Sciences

Certain partial orders on semigroups

Mario Petrich (2001)

Czechoslovak Mathematical Journal

Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups.

Characterizations of totally ordered sets by their various endomorphisms

Daniel Hort, Jan Chvalina, Jiří Moučka (2002)

Czechoslovak Mathematical Journal

We characterize totally ordered sets within the class of all ordered sets containing at least three-element chains using a simple relationship between their isotone transformations and the so called 2-, 3-, 4-endomorphisms which are introduced in the paper. Another characterization of totally ordered sets within the class of ordered sets of a locally finite height with at least four-element chains in terms of the regular semigroup theory is also given.

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