SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGS

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...

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Bibliographic Details
Main Authors: Truong Dinh Tu, Hai Dinh Hoang, Thuat Do
Format: Article
Language:English
Published: University Constantin Brancusi of Targu-Jiu 2020-03-01
Series:Surveys in Mathematics and its Applications
Subjects:
cs modules
max-min cs rings
nonsingular rings
semiprime rings
utumi rings
Online Access:http://www.utgjiu.ro/math/sma/v15/p15_09.pdf
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spelling doaj-6593bddb90184746bfa8d635f75434c42020-11-25T03:02:48ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982020-03-0115 (2020)281293SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGSTruong Dinh Tu0Hai Dinh Hoang1Thuat Do2NLP-KD Lab, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam. International Cooperation Office, Hong Duc University, 565 Quang Trung St, Dong Ve ward, Thanh Hoa city, Vietnam.Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam. and Department of Science and Technology, Nguyen Tat Thanh University, Ho Chi Minh City, Vietnam.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. http://www.utgjiu.ro/math/sma/v15/p15_09.pdfcs modulesmax-min cs ringsnonsingular ringssemiprime ringsutumi rings
collection DOAJ
language English
format Article
sources DOAJ
author Truong Dinh Tu
Hai Dinh Hoang
Thuat Do
spellingShingle Truong Dinh Tu
Hai Dinh Hoang
Thuat Do
SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGS
Surveys in Mathematics and its Applications
cs modules
max-min cs rings
nonsingular rings
semiprime rings
utumi rings
author_facet Truong Dinh Tu
Hai Dinh Hoang
Thuat Do
author_sort Truong Dinh Tu
title SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGS
title_short SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGS
title_full SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGS
title_fullStr SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGS
title_full_unstemmed SYMMETRY OF EXTENDING PROPERTIES IN NONSINGULAR UTUMI RINGS
title_sort symmetry of extending properties in nonsingular utumi rings
publisher University Constantin Brancusi of Targu-Jiu
series Surveys in Mathematics and its Applications
issn 1843-7265
1842-6298
publishDate 2020-03-01
description 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.
topic cs modules
max-min cs rings
nonsingular rings
semiprime rings
utumi rings
url http://www.utgjiu.ro/math/sma/v15/p15_09.pdf
work_keys_str_mv AT truongdinhtu symmetryofextendingpropertiesinnonsingularutumirings
AT haidinhhoang symmetryofextendingpropertiesinnonsingularutumirings
AT thuatdo symmetryofextendingpropertiesinnonsingularutumirings
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