{"title":"概括(R,S)-副模集合","authors":"Dian Ariesta Yuwaningsih, Syarifah Inayati","doi":"10.24198/jmi.v14.n2.18088.99-104","DOIUrl":null,"url":null,"abstract":"Let R and S be commutative rings with unity and M be an (R,S)-module. A proper (R,S)-submodule P of M is called a jointly prime (R,S)-submodule if for each ideal I of R, ideal J of S, and (R,S)-submodule N of M satisfy INJ ⊆ P implies IMJ ⊆ P or N ⊆ P . In this paper, we will present the definition of one generalization of jointly prime (R,S)-submodules, that is called left weakly jointly prime (R,S)-submodules. Furthermore,we will show some properties about the relationship between left weakly jointly prime (R,S)-submodules and jointly prime","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Suatu Generalisasi (R,S)-Submodul Prima Gabungan\",\"authors\":\"Dian Ariesta Yuwaningsih, Syarifah Inayati\",\"doi\":\"10.24198/jmi.v14.n2.18088.99-104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let R and S be commutative rings with unity and M be an (R,S)-module. A proper (R,S)-submodule P of M is called a jointly prime (R,S)-submodule if for each ideal I of R, ideal J of S, and (R,S)-submodule N of M satisfy INJ ⊆ P implies IMJ ⊆ P or N ⊆ P . In this paper, we will present the definition of one generalization of jointly prime (R,S)-submodules, that is called left weakly jointly prime (R,S)-submodules. Furthermore,we will show some properties about the relationship between left weakly jointly prime (R,S)-submodules and jointly prime\",\"PeriodicalId\":53096,\"journal\":{\"name\":\"Jurnal Matematika Integratif\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Jurnal Matematika Integratif\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24198/jmi.v14.n2.18088.99-104\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Jurnal Matematika Integratif","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24198/jmi.v14.n2.18088.99-104","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let R and S be commutative rings with unity and M be an (R,S)-module. A proper (R,S)-submodule P of M is called a jointly prime (R,S)-submodule if for each ideal I of R, ideal J of S, and (R,S)-submodule N of M satisfy INJ ⊆ P implies IMJ ⊆ P or N ⊆ P . In this paper, we will present the definition of one generalization of jointly prime (R,S)-submodules, that is called left weakly jointly prime (R,S)-submodules. Furthermore,we will show some properties about the relationship between left weakly jointly prime (R,S)-submodules and jointly prime