02876nam a22004455i 4500
978-0-387-78901-9
DE-He213
20180115171424.0
cr nn 008mamaa
100301s2008 xxu| s |||| 0|eng d
9780387789019
978-0-387-78901-9
10.1007/978-0-387-78901-9
doi
QA172-172.4
QA171.5
PBF
bicssc
MAT002010
bisacsh
511.33
23
Roman, Steven.
author.
Lattices and Ordered Sets
[electronic resource] /
by Steven Roman.
New York, NY :
Springer New York,
2008.
XV, 305 p.
online resource.
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Basic 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.
This 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).
Mathematics.
Algebra.
Ordered algebraic structures.
Mathematics.
Order, Lattices, Ordered Algebraic Structures.
Algebra.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9780387789002
http://dx.doi.org/10.1007/978-0-387-78901-9
ZDB-2-SMA
369754
369754
0
0
0
0
EBook
elib
elib
2018-01-15
2018-01-15
2018-01-15
EBOOK