Additive decomposition of ideals

作者：Karparvar Ali Mohammad; Amini Babak^*; Amini Afshin; Sharif Habib

来源：Journal of Algebra and Its Applications, 2018, 17(5): 1850085.

DOI：10.1142/S0219498818500858

• SNL rings
• SNP rings
• STN rings
• INL rings
• INP rings
• full matrix rings
• corner rings
• Kothe's conjecture

In this paper, we investigate decomposition of (one-sided) ideals of a unital ring R as a sum of two (one-sided) ideals, each being idempotent, nil, nilpotent, T-nilpotent, or a direct summand of R. Among other characterizations, we prove that in a polynomial identity ring every (one-sided) ideal is a sum of a nil (one-sided) ideal and an idempotent (one-sided) ideal if and only if the Jacobson radical J(R) of R is nil and R/J(R) is von Neumann regular. As a special case, these conditions for a commutative ring R are equivalent to R having zero Krull dimension. While assuming Kothe's conjecture in several occasions to be true, we also raise a question, the affirmative answer to which leads to the truth of the conjecture.

• 出版日期2018-5