Lecture Notes on Algebraic Structure of Lattice-ordered Rings

Introduction to ordered algebraic systems. 1.1 Lattices. 1.2. Lattice-ordered groups and vector lattices. 1.3. Lattice-ordered rings and algebras -- 2. Lattice-ordered algebras with a d-basis. 2.1. Examples and basic properties. 2.2. Structure theorems -- 3. Positive derivations on l-rings. 3.1. Examples and basic properties. 3.2. f-ring and its generalizations. 3.3. Matrix l-rings. 3.4. Kernel of a positive derivation -- 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 -- 5. l-ideals of l-unital lattice-ordered rings. 5.1. Maximal l-ideals. 5.2. l-ideals in commutative l-unital l-rings

Author: Jingjing Ma

Publisher: World Scientific Publishing Company Incorporated

Publication Date: May 07, 2014

Number of Pages: 247 pages

Language: English

Binding: Hardcover

ISBN-10: 9814571423

ISBN-13: 9789814571425