## Joey A. Caraquil, Joel T. Ubat, Michael P. Baldado Jr., and Rosario C. Abrasaldo, Some properties of the Ubat-space and a related structure, Eur. J. Math. Appl. 1 (2021), Article ID 1.

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Volume 1 (2021), Article ID 1

https://doi.org/10.28919/ejma.2021.1.1

Published: 20/08/2021

Abstract:

An Ubat-space is a nonempty set $U$ together with a binary operation $\ast$ satisfying: ($U1$) $x\ast (y\ast z)=(x\ast y)\ast z$ for all $x,y,z\in U$; ($U2$) There exists $y \in U$ such that $x\ast y=y\ast x=y$ for all $x \in U$; And, ($U3$) There exists $z \in U$ such that $x\ast z=z\ast x=x$ for all $x \in U$.

A $g$-group is a nonempty set $G$ together with a binary operation $\ast$ satisfying: ($g1$) $f \ast (g \ast h) = (f \ast g) \ast h$ for all $f,g,h \in G$; ($g2$) for each $g \in G$, there is $e\in G$ such that $g \ast e = e \ast g = g$ (we call $e$ an identity); and ($g3$) for each $g \in G$, there exists $h\in G$ such that $g \ast h = h \ast g = e$ for some identity $e$ described in ($g2$).

In this paper, we present some important properties of the two algebraic structures (algebra).

How to Cite:

Joey A. Caraquil, Joel T. Ubat, Michael P. Baldado Jr., and Rosario C. Abrasaldo, Some properties of the Ubat-space and a related structure, Eur. J. Math. Appl. 1 (2021), Article ID 1. https://doi.org/10.28919/ejma.2021.1.1