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Certaines relations binaires sont définies sur les demi-groupes et les demi-groupes à involution. On examine comment elles peuvent en ordonner les éléments: notamment les idempotents, les éléments réguliers au sens de von Neumann, ceux qui possédent un inverse ponctuel ou de Moore-Penrose ; et en fonction aussi de conditions sur l'involution. Ces relations peuvent alors coïncider avec les ordres naturels des idempotents et des demi-groupes inverses, avec les ordres de Drazin et de Hartwig : elles...
We introduce sturdy frames of type (2,2) algebras, which are a common generalization of sturdy semilattices of semigroups and of distributive lattices of rings in the theory of semirings. By using sturdy frames, we are able to characterize some semirings. In particular, some results on semirings recently obtained by Bandelt, Petrich and Ghosh can be extended and generalized.
For a subalgebra of a partial monounary algebra we define the quotient partial monounary algebra . Let , be partial monounary algebras. In this paper we give a construction of all partial monounary algebras such that is a subalgebra of and .
In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images.
Let τ:F → ℕ be a type of algebras, where F is a set of fundamental operation symbols and ℕ is the set of nonnegative integers. We assume that |F|≥2 and 0 ∉ (F). For a term φ of type τ we denote by F(φ) the set of fundamental operation symbols from F occurring in φ. An identity φ ≉ ψ of type τ is called clone compatible if φ and ψ are the same variable or F(φ)=F(ψ)≠. For a variety V of type τ we denote by the variety of type τ defined by all identities φ ≉ ψ from Id(V) which are either clone compatible...
J. Płonka in [12] noted that one could expect that the regularization of a variety of unary algebras is a subdirect product of and the variety of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties which are contained in the generalized variety of the so-called trap-directable algebras.
We study groupoids satisfying the identities x·xy = y and x·yz = xy·xz. Particularly, we focus our attention at subdirectlyirreducible ones, find a description and charecterize small ones.
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