in this paper, we introduce the concept of semihyperring $(r,+,cdot)$ together with a suitable partial order $le$. moreover, we introduce and study hyperideals in ordered semihyperrings. simple ordered semihyperrings are defined and its characterizations are obtained. finally, we study some properties of quasi-simple and $b$-simple ordered semihyperrings.

In this paper, we introduce the concept of semihyperring $(R,+,cdot)$ together with a suitable partial order $le$. Moreover, we introduce and study hyperideals in ordered semihyperrings. Simple ordered semihyperrings are defined and its characterizations are obtained. Finally, we study some properties of quasi-simple and $B$-simple ordered semihyperrings.

‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...

‎We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel‎, ‎that is‎, ‎every simple right $R$-module has a flat $B$-cover‎. ‎We give some properties of such rings along with examples‎. ‎We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfe...