02740nam a22004095i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153050001200169072001600181072002300197082001500220100002800235245007300263264004600336300003300382336002600415337002600441338003600467347002400503505040000527520112000927650001702047650001302064650003402077650001702111650005102128650001302179710003402192773002002226776003602246856004802282978-0-387-78901-9DE-He21320180115171424.0cr nn 008mamaa100301s2008 xxu| s |||| 0|eng d a97803877890197 a10.1007/978-0-387-78901-92doi 4aQA172-172.4 4aQA171.5 7aPBF2bicssc 7aMAT0020102bisacsh04a511.332231 aRoman, Steven.eauthor.10aLattices and Ordered Setsh[electronic resource] /cby Steven Roman. 1aNew York, NY :bSpringer New York,c2008. aXV, 305 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aBasic Theory -- Partially Ordered Sets -- Well-Ordered Sets -- Lattices -- Modular and Distributive Lattices -- Boolean Algebras -- The Representation of Distributive Lattices -- Algebraic Lattices -- Prime and Maximal Ideals; Separation Theorems -- Congruence Relations on Lattices -- Topics -- Duality for Distributive Lattices: The Priestley Topology -- Free Lattices -- Fixed-Point Theorems. aThis book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. The book has an excellent choice of topics, including a chapter on well ordering and ordinal numbers, which is not usually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises. Topic coverage includes: modular, semimodular and distributive lattices, boolean algebras, representation of distributive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more. Steven Roman is the author of many successful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), Field Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004). 0aMathematics. 0aAlgebra. 0aOrdered algebraic structures.14aMathematics.24aOrder, Lattices, Ordered Algebraic Structures.24aAlgebra.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978038778900240uhttp://dx.doi.org/10.1007/978-0-387-78901-9