Let M be a left module over a ring R and
I an ideal of R. M is called an I-supplemented module (finitely I-supplemented
module) if for every submodule (finitely generated submodule ) X of M, there is
a submodule Y of M such that $X + Y = M$, $X \cap Y \subseteq IY$ and $X \cap
Y$ is PSD in Y. This definition generalizes supplemented modules and $\delta$-supplemented
modules. We characterize I-semiregular, I-semiperfect and I-perfect rings which
are defined by Yousif and Zhou [12] using I-supplemented modules. Some well
known results are obtained as corollaries.
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 1 Şubat 2016 |
Yayımlandığı Sayı | Yıl 2016 Cilt: 45 Sayı: 1 |