Seyed Shahin Mousavi - Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Morteza Jafarpour - Mathematics Department, Vali-e-Asr University of Rafsanjan, Rafsanjan,Iran
Hojat Babaei - Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran
Irina Cristea - Center for Information Technologies and Applied Mathematics, University of Nova Gorica, Slovenia

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.

(Krasner) hyperring, strongly regular relation, lambda_e-closed hyperideal