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Title: Multiplication modules over non-commutative rings

Abstract

It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If A is a ring with commutative multiplication of right ideals, then each projective right ideal is a multiplicative module, and a finitely generated A-module M is a multiplicative module if and only if all its localizations with respect to maximal right ideals of A are cyclic modules over the corresponding localizations of A. In addition, several known results on multiplication modules over commutative rings are extended to modules over not necessarily commutative rings.

Authors:
 [1]
  1. Moscow Power Engineering Institute, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
21208364
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 194; Journal Issue: 12; Other Information: DOI: 10.1070/SM2003v194n12ABEH000788; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; COMMUTATION RELATIONS; RINGS

Citation Formats

Tuganbaev, A A. Multiplication modules over non-commutative rings. United States: N. p., 2003. Web. doi:10.1070/SM2003V194N12ABEH000788; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Tuganbaev, A A. Multiplication modules over non-commutative rings. United States. https://doi.org/10.1070/SM2003V194N12ABEH000788; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Tuganbaev, A A. 2003. "Multiplication modules over non-commutative rings". United States. https://doi.org/10.1070/SM2003V194N12ABEH000788; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21208364,
title = {Multiplication modules over non-commutative rings},
author = {Tuganbaev, A A},
abstractNote = {It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If A is a ring with commutative multiplication of right ideals, then each projective right ideal is a multiplicative module, and a finitely generated A-module M is a multiplicative module if and only if all its localizations with respect to maximal right ideals of A are cyclic modules over the corresponding localizations of A. In addition, several known results on multiplication modules over commutative rings are extended to modules over not necessarily commutative rings.},
doi = {10.1070/SM2003V194N12ABEH000788; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
url = {https://www.osti.gov/biblio/21208364}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 12,
volume = 194,
place = {United States},
year = {Wed Dec 31 00:00:00 EST 2003},
month = {Wed Dec 31 00:00:00 EST 2003}
}