William Dale Blair
Abstract
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Let R be a commutative ring with unity. Then every factor ring of R has an Artinian total quotient ring if and only if R is a direct sum of one-dimensional Noetherian domains and local Artinian rings.
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Let R be a commutative ring with unity. Then every factor ring of R has an Artinian total quotient ring if and only if R is a direct sum of one-dimensional Noetherian domains and local Artinian rings.
Key concepts: Mathematics, Artinian ring, Noncommutative ring, Principal ideal ring, Pure mathematics, Local ring, Semisimple module, Von Neumann regular ring