By Patrick J. Fleury (auth.)

ISBN-10: 3540115978

ISBN-13: 9783540115977

ISBN-10: 3540393714

ISBN-13: 9783540393719

**Read Online or Download Advances in Non-Commutative Ring Theory: Proceedings of the Twelfth George H. Hudson Symposium Held at Plattsburgh, USA, April 23–25, 1981 PDF**

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Proposition i: A right noetherian, R can be left localized left stable FLBN ring at every prime ideal P. Moreover Rp is a left stable FLBN ring. Proof: By [19, Cor. 12], P is ideal invariant, every left ideal I, K-dim(P/PI) stable, P satisfies ~ K-dim(R/I). e. for Since R is left property. By [23, Prop. 9] 49 R has a left perfect localization at P. [I0, Prop. 13]. Rp is left noetherian Suppose HOmRp(N,H ) = 0 where H is a left injective Rp-module. By [i0, Prop. 61]. is left stable, HomR(E(N),H ) = 0.

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THEOREM (4). Let then torsion radical. and so and RR for of the equivalence S be ~ r i t a equivalent rings. Let F: classes R-Mod, which implies that has finite length. ~ is R If R has finite reduced S. The proof will make use of the characterization rank given in Theorem i. has only finitely many If the torsion radical ~i is cogenerated n has finite length with respect to ~ = ni=l~ i. ,S n. RR rank (on the left), then so does Proof. R R-Mod is maximal. ,n Then if every prime torsion radical is maximal, each simple module defines a maximal nonisomorphic The then every prime torsion radical is maximal by Conversely, only finitely many maximal by is a left Noethrian ring, then be a ring with finite reduced rank (on the left) such that only if every prime torsion radical of If R this result to certain rings with finite reduced rank.

### Advances in Non-Commutative Ring Theory: Proceedings of the Twelfth George H. Hudson Symposium Held at Plattsburgh, USA, April 23–25, 1981 by Patrick J. Fleury (auth.)

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