SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGS
his paper presents the right-left symmetry of the CS and max-min CS conditions on nonsingular rings, and generalization to nonsingular modules. We prove that a ring is right nonsingular right CS and left Utumi if and only if it is left nonsingular left CS and right Utumi. A nonsingular Utumi ring is...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
University Constantin Brancusi of Targu-Jiu
2020-03-01
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Series: | Surveys in Mathematics and its Applications |
Subjects: | |
Online Access: | http://www.utgjiu.ro/math/sma/v15/p15_09.pdf |
Summary: | his paper presents the right-left symmetry of the CS and max-min CS conditions on nonsingular rings, and generalization to nonsingular modules. We prove that a ring is right nonsingular right CS and left Utumi if and only if it is left nonsingular left CS and right Utumi. A nonsingular Utumi ring is right max (resp. right min, right max-min) CS if and only if it is left min (resp. left max, left max-min) CS. In addition, a semiprime nonsingular ring is right max-min CS with finite right uniform dimension if and only if it is left max-min CS with finite left uniform dimension. |
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ISSN: | 1843-7265 1842-6298 |