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On V n -semigroups

Ze Gu, Xilin Tang (2015)

Open Mathematics

In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced. Also, we give a characterization of Vn-semigroups and investigate some properties of Vn-semigroups. Furthermore, we show that the class of Vn-semigroups is closed under direct products and homomorphic images. However, regular subsemigroups of Vn-semigroups (n ≥ 2) are not necessarily Vn-semigroups...

Some relations on the lattice of varieties of completely regular semigroups

Mario Petrich (2002)

Bollettino dell'Unione Matematica Italiana

On the lattice L ⁢ C ⁢ R of varieties of completely regular semigroups considered as algebras with the binary multiplication and unary inversion within maximal subgroups, we study the relations K l , K , K r , T l , T , T r , C and L . Here K is the kernel relation, T is the trace relation, T l and T r are the left and the right trace relations, respectively, K p = K ∩ T p for p ∈ l , r , C is the core relation and L is the local relation. We give an alternative definition for each of these relations P of the form U P V ⇔ U ∩ P ~ = V ∩ P ~ ( U , V ∈ L ( C R ) ) , for some subclasses P ~ of C ⁢ R ....

Currently displaying 61 – 80 of 111