Soft Congruence Relations over Rings
Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft congruence relations by using the soft set theory. The notions of soft quotient rings, generalized soft ideals and generalized soft q...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/541630 |
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| _version_ | 1832548995132555264 |
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| author | Xiaolong Xin Wenting Li |
| author_facet | Xiaolong Xin Wenting Li |
| author_sort | Xiaolong Xin |
| collection | DOAJ |
| description | Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft congruence relations by using the soft set theory. The notions of soft quotient rings, generalized soft ideals and generalized soft quotient rings, are introduced, and several related properties are investigated. Also, we obtain a one-to-one correspondence between soft congruence relations and idealistic soft rings and a one-to-one correspondence between soft congruence relations and soft ideals. In particular, the first, second, and third soft isomorphism theorems are established, respectively. |
| format | Article |
| id | doaj-art-4ca5688dc419489b98b2410063439d59 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-4ca5688dc419489b98b2410063439d592025-02-03T06:12:29ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/541630541630Soft Congruence Relations over RingsXiaolong Xin0Wenting Li1Department of Mathematics, Northwest University, Xi’an 710127, ChinaDepartment of Mathematics, Northwest University, Xi’an 710127, ChinaMolodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft congruence relations by using the soft set theory. The notions of soft quotient rings, generalized soft ideals and generalized soft quotient rings, are introduced, and several related properties are investigated. Also, we obtain a one-to-one correspondence between soft congruence relations and idealistic soft rings and a one-to-one correspondence between soft congruence relations and soft ideals. In particular, the first, second, and third soft isomorphism theorems are established, respectively.http://dx.doi.org/10.1155/2014/541630 |
| spellingShingle | Xiaolong Xin Wenting Li Soft Congruence Relations over Rings The Scientific World Journal |
| title | Soft Congruence Relations over Rings |
| title_full | Soft Congruence Relations over Rings |
| title_fullStr | Soft Congruence Relations over Rings |
| title_full_unstemmed | Soft Congruence Relations over Rings |
| title_short | Soft Congruence Relations over Rings |
| title_sort | soft congruence relations over rings |
| url | http://dx.doi.org/10.1155/2014/541630 |
| work_keys_str_mv | AT xiaolongxin softcongruencerelationsoverrings AT wentingli softcongruencerelationsoverrings |