The coincidence of the set of all nilpotent elements of a ring with
its prime radical has a module analogue which occurs when the zero submodule
satisfies the radical formula. A ring R is 2-primal if the set of all nilpotent
elements of R coincides with its prime radical. This fact motivates our study
in this paper, namely; to compare 2-primal submodules and submodules that
satisfy the radical formula. A demonstration of the importance of 2-primal
modules in bridging the gap between modules over commutative rings and
modules over noncommutative rings is done and new examples of rings and
modules that satisfy the radical formula are also given
Radical formula prime submodule completely prime submodule 2-primal submodule
Diğer ID | JA56YC23EG |
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Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Aralık 2015 |
Yayımlandığı Sayı | Yıl 2015 Cilt: 18 Sayı: 18 |