{"title":"半环的同余扩展性质","authors":"Yun Zhao, Yuanlan Zhou, T. Zeng","doi":"10.12988/imf.2020.912103","DOIUrl":null,"url":null,"abstract":"In this paper, we defined the congruence extension property, biideal extension property for semirings and bi-ideal semirings. Relations among the various extensions are explored. Properties of bi-ideal semirings are studied. Also, we gave some examples that a bi-ideal semiring which has the bi-ideal extension property does not have the congruence extension property, a subsemiring of a bi-ideal semiring may not be a bi-ideal semiring, etc. Finally, a necessary and sufficient condition of a special rectangular ring with congruence extension property was established. Mathematics Subject Classification: 16Y60","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Congruence extension property for semirings\",\"authors\":\"Yun Zhao, Yuanlan Zhou, T. Zeng\",\"doi\":\"10.12988/imf.2020.912103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we defined the congruence extension property, biideal extension property for semirings and bi-ideal semirings. Relations among the various extensions are explored. Properties of bi-ideal semirings are studied. Also, we gave some examples that a bi-ideal semiring which has the bi-ideal extension property does not have the congruence extension property, a subsemiring of a bi-ideal semiring may not be a bi-ideal semiring, etc. Finally, a necessary and sufficient condition of a special rectangular ring with congruence extension property was established. Mathematics Subject Classification: 16Y60\",\"PeriodicalId\":107214,\"journal\":{\"name\":\"International Mathematical Forum\",\"volume\":\"17 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematical Forum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/imf.2020.912103\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/imf.2020.912103","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we defined the congruence extension property, biideal extension property for semirings and bi-ideal semirings. Relations among the various extensions are explored. Properties of bi-ideal semirings are studied. Also, we gave some examples that a bi-ideal semiring which has the bi-ideal extension property does not have the congruence extension property, a subsemiring of a bi-ideal semiring may not be a bi-ideal semiring, etc. Finally, a necessary and sufficient condition of a special rectangular ring with congruence extension property was established. Mathematics Subject Classification: 16Y60
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