Some properties of the Ubat-space and a related structure

Abstract

An Ubat-space is a nonempty set U together with a binary operation * satisfying:A g-group is a nonempty set G together with a binary operation * satisfying:there is e ∈ G such that g * e = e * g = g (we call e an identity); and (g3) for each g ∈ G, there exists h ∈ G such that g * h = h * g = e for some identity e described in (g2).In this paper, we present some important properties of the two algebraic structures (algebra).

Some Properties of g-Groups

“…Hereafter, please refer to [3] for the other concepts. This paper is a sequel of a previously published study [1] where a new algebraic structure called g-group was introduced. Additional properties of such structure is presented and shown in this paper.…”

“…Several group-related structures such as quasigroups, generalized groups and similar structures became the favorite topic of algebra enthusiasts [6], [2], [7]. Findings from these studies were found to be applicable in other branches of mathematics such as Number Theory, Geometry, Analysis [4], Computer Science [1], etc.…”

“…A g-group is generally not a group, but groups are necessarily g-groups. Distinctions of g-groups from other group-like structures like generalized group and e-group are established in [1].…”

“…Ubat et al [1] presented Figure 1, which briefly summarizes the relationship of the × 0 1 0 0 0 1 0 1 different algebraic structure. Solid arcs represent the fact that the family in the tail is a subset of the one in the head.…”