Regular CA-Groupoids and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids) with Green Relations

Wangtao Yuan and Xiaohong Zhang
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Wangtao Yuan: Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China
Xiaohong Zhang: Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China

Mathematics, 2020, vol. 8, issue 2, 1-21

Abstract: Based on the theories of AG-groupoid, neutrosophic extended triplet (NET) and semigroup, the characteristics of regular cyclic associative groupoids (CA-groupoids) and cyclic associative neutrosophic extended triplet groupoids (CA-NET-groupoids) are further studied, and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is a regular CA-groupoid if and only if it is a CA-NET-groupoid; (2) if ( S , *) is a regular CA-groupoid, then every element of S lies in a subgroup of S , and every ? -class in S is a group; and (3) an algebraic system is an inverse CA-groupoid if and only if it is a regular CA-groupoid and its idempotent elements are commutative. Moreover, the Green relations of CA-groupoids are investigated, and some examples are presented for studying the structure of regular CA-groupoids.

Keywords: semigroup; CA-groupoid; regular CA-groupoid; neutrosophic extended triplet (NET); Green relation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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