Lecture notes on algebraic structure of lattice-ordered rings / Jingjing Ma.

Format:

Book

Author/Creator:

Ma, Jingjing, author.

Language:

English

Subjects (All):

Lattice ordered rings.

Algebra.

Physical Description:

1 online resource (258 p.)

Place of Publication:

Singapore : World Scientific, 2014.

Language Note:

English

Summary:

Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field. This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-order

Contents:

Preface; Contents; 1. Introduction to ordered algebraic systems; 1.1 Lattices; 1.2 Lattice-ordered groups and vector lattices; 1.2.1 Definitions, examples, and basic properties; 1.2.2 Structure theorems of l-groups and vector lattices; 1.3 Lattice-ordered rings and algebras; 1.3.1 Definitions, examples, and basic properties; 1.3.2 Some special l-rings; 1.3.3 l-radical and l-prime l-ideals; Exercises; 2. Lattice-ordered algebras with a d-basis; 2.1 Examples and basic properties; 2.2 Structure theorems; 2.2.1 Twisted group l-algebras; 2.2.2 l-simple case; 2.2.3 General case; Exercises

3. Positive derivations on l-rings3.1 Examples and basic properties; 3.2 f-ring and its generalizations; 3.3 Matrix l-rings; 3.4 Kernel of a positive derivation; Exercises; 4. Some topics on lattice-ordered rings; 4.1 Recognition of matrix l-rings with the entrywise order; 4.2 Positive cycles; 4.3 Nonzero f-elements in l-rings; 4.4 Quotient rings of lattice-ordered Ore domains; 4.5 Matrix l-algebras over totally ordered integral domains; 4.6 d-elements that are not positive; 4.7 Lattice-ordered triangular matrix algebras; 4.7.1 Lattice orders on T2(F) with 1 > 0

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

981-4571-43-1