arXiv subjects
Publications and source records attributed to Aiyared Iampan.
In this paper, we construct the fundamental theorem of UP-homomorphisms in UP-algebras. We also give an application of the theorem to the first, second, third and fourth UP-isomorphism theorems in UP-algebras.
In this paper, we introduce some new classes of algebras related to UP-algebras and semigroups, called a left UP-semigroup, a right UP-semigroup, a fully UP-semigroup, a left-left UP-semigroup, a right-left UP-semigroup, a left-right UP-semigroup, a right-right UP-semigroup, a fully-left UP-semigroup, a fully-right UP-semigroup, a left-fully UP-semigroup, a right-fully UP-semigroup, a fully-fully UP-semigroup, and find their examples.
Using the idea of quasi-ideals of $P$-regular nearrings, the concept of bi-ideals of $P$-regular nearrings is generalized, which is an extension of the concept of quasi-ideals of $P$-regular nearrings and some interesting characterizations of bi-ideals are obtained. As a result, we prove that every element of a bi-ideal $B$ of a $P$-regular nearring can be represented as the sum of two elements of $P$ and $Q$. Moreover, every element of the finite intersection $\displaystyle \bigcap_{i=1}^{n}B_{i}$ of bi-ideals of a $P$-regular distributive nearring $N$ can be represented as the sum of two elements of $P$ and $B_{1}NB_{2}N...NB_{n-1}NB_{n}$.
The notion of $Γ$-semirings was introduced by Murali Krishna Rao \cite{Rao} as a generalization of the notion of $Γ$-rings as well as of semirings. We have known that the notion of $Γ$-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan's work, we generalize the notion of generalized bi-$Γ$-ideals of $Γ$-semirings and investigate some related properties of generalized bi-$Γ$-ideals.