Basic Combinatorial Principles of Algebra

Ernest Shult () and David Surowski
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Ernest Shult: Kansas State University, Department of Mathematics

Chapter Chapter 2 in Algebra, 2015, pp 21-71 from Springer

Abstract: Abstract Many basic concepts used throughout Algebra have a natural home in Partially Ordered Sets (hereafter called “posets”). Aside from obvious poset residents such as Zorn’s Lemma and the well-ordered sets, some concepts are more wider roaming. Among these are the ascending and descending chain conditions, the general Jordan-Hölder Theorem (seen here as a theorem on interval measures of certain lower semillattices), Galois connections, the modular laws in lattices, and general independence notions that lead to the concepts of dimension and transcendence degree.

Keywords: Descending Chain Condition (DCC); Well-ordered Set; Galois Connection; Algebraic Interval; Ascending Chain (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-19734-0_2

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