{"title":"用拟理想刻画$\\Gamma$-半群的正则性和内正则性","authors":"Fabiana Çullhaj, Anjeza Krakulli","doi":"10.30755/nsjom.10795","DOIUrl":null,"url":null,"abstract":"The concept of regularity in Γ-semigroups is not very easy to deal with even though it shares some analogy with its analogue of semigroup theory. In this paper we establish a mechanism which translates the regularity in a Γ-semigroup (S,Γ) as the usual von Neumann regularity in an ordinary semigroup Ωγ0 that we construct in terms of (S,Γ). This enables us to characterize the regularity in Γ-semigroups by means of quasi-ideals. A similar characterization is proved for those Γ-semigroups which are regular and intra-regular. AMS Mathematics Subject Classification (2010): 20M05, 20M10, 20M12, 20M17","PeriodicalId":38723,"journal":{"name":"Novi Sad Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Some characterizations of regularity and intra-regularity of $\\\\Gamma$-semigroups by means of quasi-ideals\",\"authors\":\"Fabiana Çullhaj, Anjeza Krakulli\",\"doi\":\"10.30755/nsjom.10795\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The concept of regularity in Γ-semigroups is not very easy to deal with even though it shares some analogy with its analogue of semigroup theory. In this paper we establish a mechanism which translates the regularity in a Γ-semigroup (S,Γ) as the usual von Neumann regularity in an ordinary semigroup Ωγ0 that we construct in terms of (S,Γ). This enables us to characterize the regularity in Γ-semigroups by means of quasi-ideals. A similar characterization is proved for those Γ-semigroups which are regular and intra-regular. AMS Mathematics Subject Classification (2010): 20M05, 20M10, 20M12, 20M17\",\"PeriodicalId\":38723,\"journal\":{\"name\":\"Novi Sad Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Novi Sad Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30755/nsjom.10795\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Novi Sad Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30755/nsjom.10795","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Some characterizations of regularity and intra-regularity of $\Gamma$-semigroups by means of quasi-ideals
The concept of regularity in Γ-semigroups is not very easy to deal with even though it shares some analogy with its analogue of semigroup theory. In this paper we establish a mechanism which translates the regularity in a Γ-semigroup (S,Γ) as the usual von Neumann regularity in an ordinary semigroup Ωγ0 that we construct in terms of (S,Γ). This enables us to characterize the regularity in Γ-semigroups by means of quasi-ideals. A similar characterization is proved for those Γ-semigroups which are regular and intra-regular. AMS Mathematics Subject Classification (2010): 20M05, 20M10, 20M12, 20M17
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