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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stanley–Reisner ring ： ウィキペディア英語版 Stanley–Reisner ring In mathematics, a Stanley–Reisner ring is a quotient of a polynomial algebra over a field by a square-free monomial ideal. Such ideals are described more geometrically in terms of finite simplicial complexes. The Stanley–Reisner ring construction is a basic tool within algebraic combinatorics and combinatorial commutative algebra.〔Miller & Sturmfels (2005) p.19〕 Its properties were investigated by Richard Stanley, Melvin Hochster, and Gerald Reisner in the early 1970s. == Definition and properties == Given an abstract simplicial complex Δ on the vertex set and a field k, the corresponding Stanley–Reisner ring, or face ring, denoted k(), is obtained from the polynomial ring k() by quotienting out the ideal ''I''Δ generated by the square-free monomials corresponding to the non-faces of Δ: : $I\_\backslash Delta=(x\_\backslash ldots\; x\_:\; \backslash \backslash notin\backslash Delta),\; \backslash quad\; k()=k()/I\_\backslash Delta.$ The ideal ''I''Δ is called the Stanley–Reisner ideal or the face ideal of Δ.〔Miller & Sturmfels (2005) pp.3–5〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stanley–Reisner ring」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.