Enumeration of AG-Groupoids
نویسندگان
چکیده
Enumeration and classification of mathematical entities is an important part of mathematical research in particular in finite algebra. For algebraic structures that are more general than groups this task is often only feasible by use of computers due to the sheer number of structures that have to be considered. In this paper we present the enumeration and partial classification of AG-groupoids — groupoids in which the identity (ab)c = (cb)a holds — of up to order 6. The results are obtained with the help of the computer algebra system GAP and the constraint solver Minion by making use of both algebraic techniques as well as search pruning via symmetry breaking.
منابع مشابه
On Prime and Semiprime Ideals in Ordered AG-Groupoids
The aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered AG-groupoids with left identity. These concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered AG-groupoids, so it seems to be interesting to study them.
متن کاملOn Ideal Elements in Poe-AG-groupoid
In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal,...
متن کاملOn Quasi-Cancellativity of AG-Groupoids
Quasi-cancellativity is the generalization of cancellativity. We introduce the notion of quasi-cancellativity of semigroup into AG-groupoids. We prove that every AG-band is quasi-cancellative. We also prove the famous Burmistrovich’s Theorem for AG-groupoids that states “An AG∗∗-groupoid S is a quasi-cancellative if and only if S is a semilattice of cancellative AG∗∗-groupoids”.
متن کاملOn Uni-soft (Quasi) Ideals of AG-groupoids
In this paper we introduced the notions of uni-soft AG-groupoids, uni-soft left(right) ideals and uni-soft quasi ideals of AG-groupoids and also investigated related properties of these structures. Some interesting Characterizations of uni-soft AG-groupoids and uni-soft left(right) ideals have been explored. Mathematics Subject Classification: 42B20, 42B25, 46E30
متن کاملEnumerating Left Distributive Groupoids
Groupoids satisfying the equation x(yz) = (xy)(xz) are called left distributive, or LD-groupoids. We give an algorithm for their enumeration and prove several results on the collection of LD-groupoids extending a given monounary algebra.
متن کامل