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Title: A Comparative Study of Cyclic Associatve Left Almost Semigroups
Authors: Iqbal, Muhammad
Keywords: Physical Sciences
Issue Date: 2021
Publisher: University of Malakand, Chakdara
Abstract: A groupoid satisfying the left invertive law is called a left almost semigroup (ab breviated as LA-semigroup) or an Abel-Grassmann’s groupoid (abbreviated as AG groupoid). The structure of LA-semigroup was first introduced by M. Naseeruddin in 1970. It is a non-associative structure in general and is midway between a groupoid and a commutative semigroup. We introduced the notion of cyclic asso ciativity in LA-semigroup and studies cyclic associative LA-semigroup (abbreviated as CA-LA-semigroup) as a subclass of LA-semigroup. GAP algorithm and com putational enumeration is presented for CA-LA-semigroup. Furthermore, CA-test is presented for manual verification of a finite LA-semigroup for cyclic associativ ity. Various properties have been explored and relations of CA-LA-semigroup with other known subclasses of LA-semigroup and with other algebraic structures are established. A solution of partial condition to an open problem of left cancellative element of an LA-semigroup is proved. An open problem of quasi-cancellativity of an LA-3-band is solved. CA-LA-semigroup have been constructed from various other known algebraic structures and vice versa. The notions of equivalence re lation, (left/right) congruences, maximal idempotent-separating congruences and partial ordering are introduced in CA-LA-semigroup and characterized by their properties. The notions of various ideals, connected sets, zero, zeroid and idempoid elements are introduced and characterized in CA-LA-semigroup. Moreover, the notions of inverse CA-LA-semigroup and locally associative CA-LA-semigroup are introduced and characterized, and power associativity is studied.
Gov't Doc #: 23493
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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