{"id":{"repo_id":"mo-state","oai_identifier":"oai:bearworks.missouristate.edu:theses-1871"},"canonical_url":"https://search.dev.ndltd.org/etd/mo-state/oai:bearworks.missouristate.edu:theses-1871","repository":{"repo_id":"mo-state","name":"Missouri State University","base_url":"https://bearworks.missouristate.edu/do/oai/"},"display":{"title":"Powers of Monomial Ideals","abstract":"We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer. This is related to the well-known notion of Ratliff-Rush closures of an ideal I. We calculate the Hilbert Polynomial of certain monomial ideals. Ou approach is algebraic as well as geometric.","abstract_html":"We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer. This is related to the well-known notion of Ratliff-Rush closures of an ideal I. We calculate the Hilbert Polynomial of certain monomial ideals. Ou approach is algebraic as well as geometric.","abstract_has_math":false,"creators":["Haynes, Rhonda S."],"institution":null,"degree_name":"Master of Science in Mathematics","degree_level":"Masters","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Kishor Shah"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1999,"date_issued":"1999-05-01T07:00:00Z","date_published":"1999-05-01T07:00:00Z","updated_at":"2026-07-24T03:15:54Z","subjects":["Mathematics"],"languages":[],"rights":["© Rhonda S Haynes"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://bearworks.missouristate.edu/theses/870","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kishor Shah"]},{"key":"dc:creator","label":"Author","values":["Haynes, Rhonda S."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© Rhonda S Haynes"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://bearworks.missouristate.edu/theses/870"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer. This is related to the well-known notion of Ratliff-Rush closures of an ideal I. We calculate the Hilbert Polynomial of certain monomial ideals. Ou approach is algebraic as well as geometric."]},{"key":"dc:title","label":"Title","values":["Powers of Monomial Ideals"]}]}],"canonical_facts":{"dc:contributor":["Kishor Shah"],"dc:creator":["Haynes, Rhonda S."],"dc:description.abstract":["We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer. This is related to the well-known notion of Ratliff-Rush closures of an ideal I. We calculate the Hilbert Polynomial of certain monomial ideals. Ou approach is algebraic as well as geometric."],"dc:identifier":["https://bearworks.missouristate.edu/theses/870"],"dc:rights":["© Rhonda S Haynes"],"dc:subject":["Mathematics"],"dc:title":["Powers of Monomial Ideals"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Science in Mathematics"]},"updated_at":"2026-07-24T03:15:54Z"}