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Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings

Vijay Kumar Bhat (2013)

Czechoslovak Mathematical Journal

Let R be a ring. We recall that R is called a near pseudo-valuation ring if every minimal prime ideal of R is strongly prime. Let now σ be an automorphism of R and δ a σ -derivation of R . Then R is said to be an almost δ -divided ring if every minimal prime ideal of R is δ -divided. Let R be a Noetherian ring which is also an algebra over ℚ ( ℚ is the field of rational numbers). Let σ be an automorphism of R such that R is a σ ( * ) -ring and δ a σ -derivation of R such that σ ( δ ( a ) ) = δ ( σ ( a ) ) for all a ∈ R . Further, if for any...

New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.

Carl Faith (1996)

Publicacions Matemàtiques

A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.

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