{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","description":"This cluster of papers focuses on the study of properties and structures of commutative rings, including topics such as zero-divisor graphs, Armendariz rings, idealization, Baer rings, nil-clean rings, annihilator ideals, quasi-Baer rings, factorization theory, triangular matrix representations, and semistar operations.","keywords":[{"id":"https://openalex.org/keywords/ring-theory","display_name":"ring theory","score":0.7855},{"id":"https://openalex.org/keywords/commutative-rings","display_name":"commutative rings","score":0.6679},{"id":"https://openalex.org/keywords/module-theory","display_name":"module theory","score":0.7851},{"id":"https://openalex.org/keywords/commutative-algebra","display_name":"commutative algebra","score":0.2751},{"id":"https://openalex.org/keywords/noncommutative-rings","display_name":"noncommutative rings","score":0.7092},{"id":"https://openalex.org/keywords/prime-ideals","display_name":"prime ideals","score":0.4773},{"id":"https://openalex.org/keywords/integral-domains","display_name":"integral domains","score":0.705},{"id":"https://openalex.org/keywords/polynomial-rings","display_name":"polynomial rings","score":0.2435},{"id":"https://openalex.org/keywords/endomorphism-rings","display_name":"endomorphism rings","score":0.5971},{"id":"https://openalex.org/keywords/idempotents","display_name":"idempotents","score":0.3332},{"id":"https://openalex.org/keywords/group-rings","display_name":"group rings","score":0.4334},{"id":"https://openalex.org/keywords/prime-rings","display_name":"prime rings","score":0.8167},{"id":"https://openalex.org/keywords/jacobson-radical","display_name":"Jacobson radical","score":0.7079},{"id":"https://openalex.org/keywords/injective-modules","display_name":"injective modules","score":0.7076},{"id":"https://openalex.org/keywords/finitely-generated-modules","display_name":"finitely generated modules","score":0.3984},{"id":"https://openalex.org/keywords/matrix-rings","display_name":"matrix rings","score":0.8001},{"id":"https://openalex.org/keywords/noetherian-rings","display_name":"Noetherian rings","score":0.5207},{"id":"https://openalex.org/keywords/projective-modules","display_name":"projective modules","score":0.4552},{"id":"https://openalex.org/keywords/zero-divisors","display_name":"zero divisors","score":0.5702},{"id":"https://openalex.org/keywords/ring-extensions","display_name":"ring extensions","score":0.8151},{"id":"https://openalex.org/keywords/division-rings","display_name":"division rings","score":0.609},{"id":"https://openalex.org/keywords/semiprime-rings","display_name":"semiprime rings","score":0.8453},{"id":"https://openalex.org/keywords/near-rings","display_name":"near-rings","score":0.7371},{"id":"https://openalex.org/keywords/dedekind-domains","display_name":"Dedekind domains","score":0.5318},{"id":"https://openalex.org/keywords/ideal-theory","display_name":"ideal theory","score":0.3116}],"legacy_keywords":"Zero-Divisor Graphs; Armendariz Rings; Idealization; Baer Rings; Nil-Clean Rings; Annihilator Ideals; Quasi-Baer Rings; Factorization Theory; Triangular Matrix Representations; Semistar Operations","ids":{"openalex":"https://openalex.org/T11703","wikipedia":"https://en.wikipedia.org/wiki/Commutative_ring"},"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"},"siblings":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research"},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities"},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra"},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications"}],"works_count":73923,"cited_by_count":508447,"works_api_url":"https://api.openalex.org/works?filter=topics.id:T11703","updated_date":"2026-10-22T03:01:35","created_date":"2024-01-23T15:27:11"}