Normality on Jacobson and nil radicals
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This article concerns the normal property of elements on Jacobson and nil radicals which are generalizations of commutativity. A ring is said to be {\it right njr} if it satisfies the normal property on the Jacobson radical. Similarly a ring is said to be {\it right nunr} (resp., {\it right nlnr}) if it satisfies the normal property on the upper (resp., lower) nilradical. We investigate the relations between right duo property and the normality on Jacobson (nil) radicals. Related examples are investigated in the procedure of studying the structures of right njr, nunr, and nlnr rings.
Abstract
This article concerns the normal property of elements on Jacobson and nil radicals which are generalizations of commutativity. A ring is said to be {\it right njr} if it satisfies the normal property on the Jacobson radical. Similarly a ring is said to be {\it right nunr} (resp., {\it right nlnr}) if it satisfies the normal property on the upper (resp., lower) nilradical. We investigate the relations between right duo property and the normality on Jacobson (nil) radicals. Related examples are investigated in the procedure of studying the structures of right njr, nunr, and nlnr rings.
참고문헌 (11)
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