Abstract
Cyclic associative groupoids (CA-groupoids) and Type-2 cyclic associative groupoids (T2CA-groupoids) are two types of non-associative groupoids which satisfy cyclic associative law and type-2 cyclic associative law, respectively. In this paper, we prove two theorems that weak cancellativity is cancellativity and right quasi-cancellativity is left quasi-cancellativity in a CA-groupoid, thus successfully solving two open problems. Moreover, the relationships among separativity, quasi-cancellativity and commutativity in a CA-groupoid are discussed. Finally, we study the various cancellativities of T2CA-groupoids such as power cancellativity, quasi-cancellativity and cancellativity. By determining the relationships between them, we can illuminate the structure of T2CA-groupoids.
Funder
National Natural Science Foundation of China
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference32 articles.
1. On almost semigroups;Kazim;Aligarh Bull. Math.,1972
2. A kind of non-associative groupoids and quasi neutrosophic extended triplet groupoids (QNET-groupoids);Zhang;Neutrosophic Sets Syst.,2020
3. Some functional equations related with the associative law;Hosszú;Publ. Math. Debrecen,1954
4. CM solutions of some functional equations of associative type;Maksa;Annales Univ. Sci. Budapest. Sect. Comp.,2004
5. Power series solutions of Tarski’s associativity law and of the cyclic associativity law
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