软半环的软同态和软商半环
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摘要
二元关系,特别地,等价关系在数学和信息科学中都起着很重要的作用.软集理论最早是由Molodtsov提出来的,它作为一般地数学工具来处理不确性问题.用软集理论来研究和学习软同余关系.首先介绍了软商半环的概念,然后用软同余关系来建立几个软半环的软同构定理.
Binary relations,in particular,equivalence relations play an important role in both mathematics and information science.The concept of soft set is first initiated by Molodtsov as a general mathematical frame work for dealing with uncertainty.In this paper,we initiate the study of soft congruence relations by using the soft set theory.We first show the notion of soft quotient heminings,and then we establish several soft isomorphism theorems for soft hemirings using soft congruence relations.
Binary relations,in particular,equivalence relations play an important role in both mathematics and information science.The concept of soft set is first initiated by Molodtsov as a general mathematical frame work for dealing with uncertainty.In this paper,we initiate the study of soft congruence relations by using the soft set theory.We first show the notion of soft quotient heminings,and then we establish several soft isomorphism theorems for soft hemirings using soft congruence relations.
引文
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[2]Jun Y B.Soft BCK/BCI-algebras[J].Comput Math Appl,2008,56(5):1408-1413.
[3]Acar U,Fatih K,Bekir T.Soft sets and soft rings[J].Comput Math Appl,2010,59(11):3458-3463
[4]Liu X,Xiang D,Zhan J.Isomorphism theorems for soft rings[J].Algebra Colloquium,2012,19(4):649-656.
[5]Liu X,Xiang D,Zhan J.Fuzzy isomorphism theorems of soft rings[J].Neural Comput Appl,2012,21(2):391-397.
[6]Feng F,Ali M I,Shabir M.Soft relations applied to semigroups[J].Filomat,2013,27(7):1183-1196.
[7]Xin X,Li W.Soft congruence relations over rings[J].The Scientific World Journal,Volume 2014,Article ID,541630,9 pages.
[8]Feng F,Jun Y B,Zhao X.Z.Soft semirings[J].Comput Math Appl,2008,56(10):2621-2628.
[2]Jun Y B.Soft BCK/BCI-algebras[J].Comput Math Appl,2008,56(5):1408-1413.
[3]Acar U,Fatih K,Bekir T.Soft sets and soft rings[J].Comput Math Appl,2010,59(11):3458-3463
[4]Liu X,Xiang D,Zhan J.Isomorphism theorems for soft rings[J].Algebra Colloquium,2012,19(4):649-656.
[5]Liu X,Xiang D,Zhan J.Fuzzy isomorphism theorems of soft rings[J].Neural Comput Appl,2012,21(2):391-397.
[6]Feng F,Ali M I,Shabir M.Soft relations applied to semigroups[J].Filomat,2013,27(7):1183-1196.
[7]Xin X,Li W.Soft congruence relations over rings[J].The Scientific World Journal,Volume 2014,Article ID,541630,9 pages.
[8]Feng F,Jun Y B,Zhao X.Z.Soft semirings[J].Comput Math Appl,2008,56(10):2621-2628.