頁籤選單縮合
題 名 | Some Applications of Zorn's Lemma in Algebra |
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作 者 | Anderson, D. D.; Dobbs, David E.; Zafrullah, Muhammad; | 書刊名 | Tamkang Journal of Mathematics |
卷 期 | 40:2 2009.夏[民98.夏] |
頁 次 | 頁139-150 |
分類號 | 315 |
關鍵詞 | Zorn's Lemma; Submodule; Projective; Injective; Semisimple; Flat; Finitely generated; Subalgebra; Going-down; Going-up; Subgroup; Integral domain; Star operation; *-Prüfer domain; *-Krull domain; Suboboject; |
語 文 | 英文(English) |
英文摘要 | We indicate some new applications of Zorn's Lemma to a number of algebraic areas. Specifically, we show that a property P holds for all the subobjects of a given object if and only if P supports both the chain condition from Zorn's Lemma and some finitistic conditions on subobjects that have the flavor of mathematical induction. The specific algebraic contexts considered are modules, sets, groups, algebras, and integral domains. Particular emphasis is given to applications involving star operations on integral domains. |
本系統中英文摘要資訊取自各篇刊載內容。