{"title":"无扭阿贝尔半群环","authors":"Ryuki Matsuda","doi":"10.5036/BFSIU1968.18.23","DOIUrl":null,"url":null,"abstract":"If Γ is a nonempty set which is associative under an operation on Γ, we say that Γ is an associative set. We call a torsion-free cancellative commutative associative set S〓{0} a semigroup. We call a commutative ring A with the identity 1 a ring. Let A be a ring, S a semigroup. The semigroup ring A[X;S] of S over A is the ring of elements a1Xα1+...+anXαn, where ai∈A and αi∈S for each i. A general reference on semigroup rings is [6]. The aim of this paper is to continue [12].","PeriodicalId":141145,"journal":{"name":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1978-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"38","resultStr":"{\"title\":\"Torsion-free abelian semigroup rings IX\",\"authors\":\"Ryuki Matsuda\",\"doi\":\"10.5036/BFSIU1968.18.23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"If Γ is a nonempty set which is associative under an operation on Γ, we say that Γ is an associative set. We call a torsion-free cancellative commutative associative set S〓{0} a semigroup. We call a commutative ring A with the identity 1 a ring. Let A be a ring, S a semigroup. The semigroup ring A[X;S] of S over A is the ring of elements a1Xα1+...+anXαn, where ai∈A and αi∈S for each i. A general reference on semigroup rings is [6]. The aim of this paper is to continue [12].\",\"PeriodicalId\":141145,\"journal\":{\"name\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"38\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/BFSIU1968.18.23\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/BFSIU1968.18.23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
If Γ is a nonempty set which is associative under an operation on Γ, we say that Γ is an associative set. We call a torsion-free cancellative commutative associative set S〓{0} a semigroup. We call a commutative ring A with the identity 1 a ring. Let A be a ring, S a semigroup. The semigroup ring A[X;S] of S over A is the ring of elements a1Xα1+...+anXαn, where ai∈A and αi∈S for each i. A general reference on semigroup rings is [6]. The aim of this paper is to continue [12].
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