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- Title
Some Congruences on CA-AG-groupoids.
- Authors
Iqbal, Muhammad; Ahmad, Imtiaz
- Abstract
An AG-groupoid S satisfying the identity x(yz) = z(xy) for all x, y, z ∈ S is called a CA-AG-groupoid. In this article the notions of equivalence relation and congruence is extended to CA-AG-groupoids and various congruences on CA-AG-groupoid and inverse CA-AG-groupoid are defined and investigated. Furthermore, it is shown that a suitably defined relation ρ on inverse CA-AG-groupoid S is a maximal idempotentseparating congruence, that S/ρ is fundamental and that the semilattice of idempotents of S is isomorphic to the semilattice of idempotents on S/ρ.
- Subjects
GROUPOIDS; EQUIVALENCE relations (Set theory); SELF-congruence; IDEMPOTENTS; IDENTITIES (Mathematics)
- Publication
Punjab University Journal of Mathematics, 2019, Vol 51, Issue 3, p71
- ISSN
1016-2526
- Publication type
Article