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2015•Journal of Algebra and Its ApplicationsRequires access

When every pure ideal is projective

Jiangsheng Hu, Haiyu Liu, Yuxian Geng

Open publisher page 4 citations

Abstract

In this paper, we study the class of rings in which every pure ideal is projective. We refer to rings with this property as PIP-rings. Some properties and examples of PIP-rings are given. When R is a PIP-ring, some new homological dimensions for complexes are given. As applications, we give some new characterizations of von Neumann regular rings, F-rings and semisimple Artinian rings.

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What this paper is about

In this paper, we study the class of rings in which every pure ideal is projective. We refer to rings with this property as PIP-rings. Some properties and examples of PIP-rings are given. When R is a PIP-ring, some new homological dimensions for complexes are given. As applications, we give some new characterizations of von Neumann regular rings, F-rings and semisimple Artinian rings.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we study the class of rings in which every pure ideal is projective. We refer to rings with this property as PIP-rings. Some properties and examples of PIP-rings are given. When R is a PIP-ring, some new homological dimensions for complexes are given. As applications, we give some new characterizations of von Neumann regular rings, F-rings and semisimple Artinian rings.

Key concepts: Mathematics, Semisimple module, Von Neumann regular ring, Artinian ring, Ideal (ethics), Projective module, Pure mathematics, Von Neumann architecture

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