Abstract
In this paper, we introduce transposition regularity into AG-groupoids, and a variety of transposition regular AG-groupoids (L1/R1/LR, L2/R2/L3/R3-groupoids) are obtained. Their properties and structures are discussed by their decomposition theorems: (1) L1/R1-transposition regular AG-groupoids are equivalent to each other, and they can be decomposed into the union of disjoint Abelian subgroups; (2) L1/R1-transposition regular AG-groupoids are LR-transposition regular AG-groupoids, and an example is given to illustrate that not every LR-transposition regular AG-groupoid is an L1/R1-transposition regular AG-groupoid; (3) an AG-groupoid is an L1/R1-transposition regular AG-groupoid if it is an LR-transposition regular AG-groupoid satisfying a certain condition; (4) strong L2/R3-transposition regular AG-groupoids are equivalent to each other, and they are union of disjoint Abelian subgroups; (5) strong L3/R2-transposition regular AG-groupoids are equivalent to each other and they can be decomposed into union of disjoint AG subgroups. Their relations are discussed. Finally, we introduce various transposition regular AG-groupoid semigroups and discuss the relationships among them and the commutative Clifford semigroup as well as the Abelian group.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
