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Congruences on completely inverse AG**-groupoids
Authors: W. A. Dudek, R. S. Gigon
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Abstract
By a completely inverse AG**-groupoid we mean an inverse AG**-groupoid A satisfying the identity xx*=x*x, where x* denotes a unique element of A such that x=(xx*)x and x*=(x*x)x*.$ We show that the set of all idempotents of such groupoid forms a semilattice and the Green's relations H,L,R,D and J coincide on A. The main result of this note says that any completely inverse AG**-groupoid meets the famous Lallement's Lemma for regular semigroups. Finally, we show that the Green's relation H is both the least semilattice congruence and the maximum idempotent-separating congruence on any completely inverse AG**-groupoid.Fulltext
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Contents
- Bipolar fuzzy Lie superalgebras
- Recursively r-differentiable quasigroups within S-systems and MDS-codes
- A characterization of binary invertible algebras of various types of linearity
- Generalized IP-loops
- D-loops
- Prime and weakly prime ideals in semirings
- Congruences on completely inverse AG**-groupoids
- Construction of subdirectly irreducible SQS-skeins
- Clifford congruences on an idempotent-surjective R-semigroup
- A new characterization of Osborn-Buchsteiner loops
- Left quasi-regular and intra-regular ordered semigroups using fuzzy ideals
- On fuzzy ordered semigroups
- On finite loops whose inner mapping groups are direct products of dihedral groups and abelian groups
- New signature scheme based on difficulty of finding roots
- Some remarks on Abel-Grassmann's groupsC
- Polyadic groups and automorphisms of cyclic extensions
