2014/03/10 by Muhammad Rashad Amanullah, Imtiaz Ahmad, Amanullah, Muhammad Rashad +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #20N05 20L05 #20N99 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #math.GR #msc:20L05 #msc:20N05 #msc:20N99 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1403.2304
12 pages
openalex publication_date 2014/03/10 · arxiv created 2015/02/10 · arxiv updated 2016/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The binary operation of usual addition is associative in all common matrices over R. However, here we define a binary operation of addition in matrices over Zn which present the concept of nonassociativity. These structures form Matrix AG-groupoids and Matrix AG-groups over modulo integers Zn. We show that both these structures exist for every integer n geq 3, and explore some of their properties like: (i). Every matrix AG-groupoid Gn AG(t, u), is transitively commutative AG-groupoid and is a cancellative AG-groupoid if n is prime. (ii). Every matrix AG-groupoid of Type GAG-II(n) is T3-AG-groupoid. (iii). A matrix AG-groupoid GnAG(t, u) is an AG-band, if t + u = 1(mod n).