{"title":"关于合并代数的最大(理想)图","authors":"Zinat Rastgar, K. Khashyarmanesh, M. Afkhami","doi":"10.47443/dml.2022.095","DOIUrl":null,"url":null,"abstract":"Let f : A → B be a ring homomorphism of the commutative rings A and B with identities. Let J be an ideal of B . The amalgamation of A with B along J with respect to f is a subring of A × B given by A (cid:46)(cid:47) f J := { ( a, f ( a )+ j ) | a ∈ A , j ∈ J } . In this paper, we investigate the comaximal ideal graph and the comaximal graph of the amalgamated algebra A (cid:46)(cid:47) f J . In particular, we determine the Jacobson radical of A (cid:46)(cid:47) f J , characterize the diameter of the comaximal ideal graph of A (cid:46)(cid:47) f J , and investigate the clique number as well as the chromatic number of this graph.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Comaximal (Ideal) Graph Associated With Amalgamated Algebra\",\"authors\":\"Zinat Rastgar, K. Khashyarmanesh, M. Afkhami\",\"doi\":\"10.47443/dml.2022.095\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let f : A → B be a ring homomorphism of the commutative rings A and B with identities. Let J be an ideal of B . The amalgamation of A with B along J with respect to f is a subring of A × B given by A (cid:46)(cid:47) f J := { ( a, f ( a )+ j ) | a ∈ A , j ∈ J } . In this paper, we investigate the comaximal ideal graph and the comaximal graph of the amalgamated algebra A (cid:46)(cid:47) f J . In particular, we determine the Jacobson radical of A (cid:46)(cid:47) f J , characterize the diameter of the comaximal ideal graph of A (cid:46)(cid:47) f J , and investigate the clique number as well as the chromatic number of this graph.\",\"PeriodicalId\":36023,\"journal\":{\"name\":\"Discrete Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47443/dml.2022.095\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2022.095","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Comaximal (Ideal) Graph Associated With Amalgamated Algebra
Let f : A → B be a ring homomorphism of the commutative rings A and B with identities. Let J be an ideal of B . The amalgamation of A with B along J with respect to f is a subring of A × B given by A (cid:46)(cid:47) f J := { ( a, f ( a )+ j ) | a ∈ A , j ∈ J } . In this paper, we investigate the comaximal ideal graph and the comaximal graph of the amalgamated algebra A (cid:46)(cid:47) f J . In particular, we determine the Jacobson radical of A (cid:46)(cid:47) f J , characterize the diameter of the comaximal ideal graph of A (cid:46)(cid:47) f J , and investigate the clique number as well as the chromatic number of this graph.
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