Generalizations of von Neumann regular rings, <i>PP</i> rings, and Baer rings

doi:10.1007/s11464-016-0523-1

Front. Math. China

2016, Vol. 11

Issue (2) : 377-400 https://doi.org/10.1007/s11464-016-0523-1

RESEARCH ARTICLE

Generalizations of von Neumann regular rings, PP rings, and Baer rings

Lixin MAO(

)

Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, China

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Abstract

We introduce the notions of IDS modules, IP modules, and Baer^*modules, which are new generalizations of von Neumann regular rings, PPrings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer? modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer^*modules.

Keywords IDS Module IP module Baer? module von Neumann regular ring PP ring Baer ring

Corresponding Author(s): Lixin MAO

Issue Date: 18 April 2016

Cite this article:

Lixin MAO. Generalizations of von Neumann regular rings, PP rings, and Baer rings[J]. Front. Math. China, 2016, 11(2): 377-400.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0523-1
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I2/377

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