lambda

In this paper first, we introduce and analyze the strongly regular relations $\lambda^*_{e}$ and $\Lambda^*_{e}$ on a hyperring such that the derived quotient ring is unitary and unitary commutative, respectively. Next, we define and study the notion of $\lambda_e$-parts in a hyperring and  characterize the $\lambda_e$-parts in a $\lambda_e$-strong hyperring $R$. Finally, we introduce the notion of $\lambda_e$-closed hyperideal in a hyperring and study some of its fundamental properties in Krasner hyperrings.

Arenas et al. [1] introduced the notion of lambda-closed sets as a generalization of locally closed sets. In this paper, we introduce the notions of lambda-locally closed sets, Lambda_lambda-closed sets and lambda_g-closed sets and obtain some decompositions of closed sets and continuity in topological spaces.