On a Generalization of Semisimple Modules
Künye
AGHAYEV, Nazım, Cesim ÇELİK & Tahire ÖZEN. "On a Generalization of Semisimple Modules". Proceedings of the Indian Academy of Sciences-Mathematical Sciences, 128.2 (2018): 1-10.Özet
Let R be a ring with identity. A module MR is called an r-semisimple
module if for any right ideal I of R, MI is a direct summand of MR which is a
generalization of semisimple and second modules.We investigate when an r-semisimple
ring is semisimple and prove that a ring R with the number of nonzero proper ideals ≤4
and J (R) = 0 is r -semisimple. Moreover, we prove that R is an r-semisimple ring if
and only if it is a direct sum of simple rings and we investigate the structure of module
whenever R is an r-semisimple ring.
