{"cited_by_count":233351,"description":"This cluster of papers focuses on the algebraic properties of monomial ideals, including their graded Betti numbers, local cohomology modules, symbolic powers, edge ideals, Cohen-Macaulay modules, Stanley depth, toric algebra, regularity bounds, and their connections to combinatorial topology.","display_name":"Commutative Algebra and Its Applications","domain_id":"3","external_ids":{"openalex":"https://openalex.org/T12069","wikipedia":"https://en.wikipedia.org/wiki/Monomial_ideal"},"field_id":"26","id":"T12069","keywords":[{"display_name":"commutative algebra","id":"commutative-algebra","score":0.3526,"url":"https://openalex.org/keywords/commutative-algebra"},{"display_name":"monomial ideals","id":"monomial-ideals","score":0.875,"url":"https://openalex.org/keywords/monomial-ideals"},{"display_name":"Hilbert functions","id":"hilbert-functions","score":0.741,"url":"https://openalex.org/keywords/hilbert-functions"},{"display_name":"polynomial rings","id":"polynomial-rings","score":0.2382,"url":"https://openalex.org/keywords/polynomial-rings"},{"display_name":"local cohomology","id":"local-cohomology","score":0.6993,"url":"https://openalex.org/keywords/local-cohomology"},{"display_name":"local rings","id":"local-rings","score":0.4453,"url":"https://openalex.org/keywords/local-rings"},{"display_name":"Cohen-Macaulay rings","id":"cohen-macaulay-rings","score":0.8891,"url":"https://openalex.org/keywords/cohen-macaulay-rings"},{"display_name":"finitely generated modules","id":"finitely-generated-modules","score":0.3353,"url":"https://openalex.org/keywords/finitely-generated-modules"},{"display_name":"Castelnuovo-Mumford regularity","id":"castelnuovo-mumford-regularity","score":0.86,"url":"https://openalex.org/keywords/castelnuovo-mumford-regularity"},{"display_name":"Hilbert series","id":"hilbert-series","score":0.4782,"url":"https://openalex.org/keywords/hilbert-series"},{"display_name":"numerical semigroups","id":"numerical-semigroups","score":0.6235,"url":"https://openalex.org/keywords/numerical-semigroups"},{"display_name":"edge ideals","id":"edge-ideals","score":0.9779,"url":"https://openalex.org/keywords/edge-ideals"},{"display_name":"minimal free resolutions","id":"minimal-free-resolutions","score":0.8386,"url":"https://openalex.org/keywords/minimal-free-resolutions"},{"display_name":"Betti numbers","id":"betti-numbers","score":0.2205,"url":"https://openalex.org/keywords/betti-numbers"},{"display_name":"local cohomology modules","id":"local-cohomology-modules","score":0.9528,"url":"https://openalex.org/keywords/local-cohomology-modules"},{"display_name":"Gorenstein rings","id":"gorenstein-rings","score":0.7096,"url":"https://openalex.org/keywords/gorenstein-rings"},{"display_name":"Noetherian rings","id":"noetherian-rings","score":0.2924,"url":"https://openalex.org/keywords/noetherian-rings"},{"display_name":"Noetherian local rings","id":"noetherian-local-rings","score":0.8849,"url":"https://openalex.org/keywords/noetherian-local-rings"},{"display_name":"associated primes","id":"associated-primes","score":0.7686,"url":"https://openalex.org/keywords/associated-primes"},{"display_name":"commutative Noetherian rings","id":"commutative-noetherian-rings","score":0.609,"url":"https://openalex.org/keywords/commutative-noetherian-rings"},{"display_name":"complete intersections","id":"complete-intersections","score":0.2886,"url":"https://openalex.org/keywords/complete-intersections"},{"display_name":"Rees algebra","id":"rees-algebra","score":0.8943,"url":"https://openalex.org/keywords/rees-algebra"},{"display_name":"free resolutions","id":"free-resolutions","score":0.6483,"url":"https://openalex.org/keywords/free-resolutions"},{"display_name":"syzygies","id":"syzygies","score":0.2737,"url":"https://openalex.org/keywords/syzygies"},{"display_name":"graded Betti numbers","id":"graded-betti-numbers","score":0.8923,"url":"https://openalex.org/keywords/graded-betti-numbers"}],"legacy_keywords":["Monomial Ideals","Graded Betti Numbers","Local Cohomology Modules","Symbolic Powers","Edge Ideals","Cohen-Macaulay Modules","Stanley Depth","Toric Algebra","Regularity Bounds","Combinatorial Topology"],"openalex_id":"https://openalex.org/T12069","source_created_date":"2024-01-23T15:27:12","source_updated_date":"2026-10-17T03:02:00","subfield_id":"2602","url":"/topics/T12069","works_api_url":"https://api.openalex.org/works?filter=topics.id:T12069","works_count":24973,"label":"Commutative Algebra and Its Applications","provider":"openalex","revision":"a9703e50c168f0aa","taxonomy_revision":"f050b5d4780b1289","title":"Commutative Algebra and Its Applications","kind":"topic-directory","aeo_cohort":"topic-directory","catalogue_revision":"f050b5d4780b1289","numeric_address":"36249558350719097","address_version":"morton4x16-v1","coordinates":[3,26,2602,12069],"answer_status":"Directory metadata; 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