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NJ-Abelian Rings: an Abelian-Like Approach
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This article extends the concept of NJ-semicommutative rings to introduce the broader class of NJ-abelian rings, which are defined by properties involving nilpotent elements and the Jacobson radical. We investigate the unique algebraic properties of NJ-abelian rings and analyze their relationships with various types of rings, including abelian, reduced, J-clean, local, and Dedekind-finite rings. In particular, we show that every NJ-semicommutative ring is NJ-abelian, much like every semicommutative ring is abelian.
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Title: NJ-Abelian Rings: an Abelian-Like Approach
Description:
This article extends the concept of NJ-semicommutative rings to introduce the broader class of NJ-abelian rings, which are defined by properties involving nilpotent elements and the Jacobson radical.
We investigate the unique algebraic properties of NJ-abelian rings and analyze their relationships with various types of rings, including abelian, reduced, J-clean, local, and Dedekind-finite rings.
In particular, we show that every NJ-semicommutative ring is NJ-abelian, much like every semicommutative ring is abelian.
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