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1960•Proceedings of the American Mathematical SocietyRequires access

Differentiably simple rings

Edward C. Posner

Open publisher page 45 citations

Abstract

Let R be a ring and 2D a family of derivations of R into itself.We call R differentiably simple under 2D if R2^0 and if R has no twosided ideal (other than 0 and R) sent into itself under every derivation of the family 20 (i.e., has no differential ideal).We shall call R differentiably simple, usually without specifying 2D.The purpose of this paper is to explore the analogy between simple rings and differentiably simple rings.

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What this paper is about

Let R be a ring and 2D a family of derivations of R into itself.We call R differentiably simple under 2D if R2^0 and if R has no twosided ideal (other than 0 and R) sent into itself under every derivation of the family 20 (i.e., has no differential ideal).We shall call R differentiably simple, usually without specifying 2D.The purpose of this paper is to explore the analogy between simple rings and differentiably simple rings.

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Available abstract

Let R be a ring and 2D a family of derivations of R into itself.We call R differentiably simple under 2D if R2^0 and if R has no twosided ideal (other than 0 and R) sent into itself under every derivation of the family 20 (i.e., has no differential ideal).We shall call R differentiably simple, usually without specifying 2D.The purpose of this paper is to explore the analogy between simple rings and differentiably simple rings.

Key concepts: Simple (philosophy), Ideal (ethics), Simple ring, Mathematics, Analogy, Ring (chemistry), Pure mathematics, Calculus (dental)

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