论文信息 - Some Structural Properties of AG-Groups

Some Structural Properties of AG-Groups

An AG-group ( an AG-groupoid with left identity and inverses) is a nonassociative structure in general midway between a quasigroup and an abelian group. This paper is meant to re-start the study of AG-groups. We prove that for an AG-group associativity and commutativity imply each other. Nonassociative AG-groups can never be power associative. The duality between left AG-groups and right AG-groups is also discussed.

Asif Ali | Muhammad Raza Shah

[1] Naseeruddin,et al. On almost semigroups , 1977 .

[2] Muhammad Sarwar. CONDITIONS FOR LA-SEMIGROUPS TO RESEMBLE ASSOCIATIVE STRUCTURES , 1993 .

[3] John Slaney,et al. Counting loops with the inverse property , 2008 .

[4] Tariq Shah,et al. On the Cancellativity of AG-Groupoids , 2011 .