nach der Bestellung gedruckt Neuware - Printed after ordering - Over the last 40 years, interest has arisen in the study of modern algebraic systems like: rings, modules over rings. The concept 'Dimension' of a vector space, when generalized to modules becomes the concept 'Goldie Dimension'. This dimension concept was studied by several authors from different continents. This Goldie Dimension Theory is not suitable to develop dimension theory for rings with respect to two sided ideals in case of associative rings (but not commutative rings). A suitable concept 'Finite Dimension' was introduced and studied in Ring Theory. This Monograph covers a vital study of several important concepts like: g-prime radical, Zero Square Dimension, Zero Square Fuzzy Ideal, Principal Ideal Graph of a Ring, Prime Graph of a Ring. The concepts Principal Ideal Graph and Prime Ideal Graph form two different new bridges between 'Graph Theory' and the algebraic concept 'Ring'. Necessary examples were included. This Monograph is certainly attracts the interest of all algebraists, Ring Theorists, in particular. This Monograph is a more valuable addition not only to the institutional libraries, but also to each personal library of every algebraist of the world.

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Bibliographic Details

Title: Dimension and Graph Theoretic Aspects of Rings (Monograph) : Prime Ideal, Finite Goldie Dimension, Zero Square Dimension, Zero Square Fuzzy Ideal, Principal Ideal Graph, Prime Graph of a Ring
Publisher: VDM Verlag Dr. M�ller
Publication Date: 2011
Language: English
ISBN 10: 3639305582
ISBN 13: 9783639305586
Binding: Taschenbuch
Condition: Neu
Dimensions: 220 millimeters width by 150 millimeters height by 10 millimeters depth
Weight: 251 grams

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Synopsis

Over the last 40 years, interest has arisen in the study of modern algebraic systems like: rings, modules over rings. The concept "Dimension" of a vector space, when generalized to modules becomes the concept "Goldie Dimension". This dimension concept was studied by several authors from different continents. This Goldie Dimension Theory is not suitable to develop dimension theory for rings with respect to “two sided ideals” in case of associative rings (but not commutative rings). A suitable concept "Finite Dimension" was introduced and studied in Ring Theory. This Monograph covers a vital study of several important concepts like: g-prime radical, Zero Square Dimension, Zero Square Fuzzy Ideal, Principal Ideal Graph of a Ring, Prime Graph of a Ring. The concepts Principal Ideal Graph and Prime Ideal Graph form two different new bridges between "Graph Theory" and the algebraic concept "Ring". Necessary examples were included. This Monograph is certainly attracts the interest of all algebraists, Ring Theorists, in particular. This Monograph is a more valuable addition not only to the institutional libraries, but also to each personal library of every algebraist of the world.

About the Author

Prof. Dr Bhavanari Satyanarayana, FAPAS, Awards: AP Scientist, Glory of India (in Thailand, 2011), 28 yr Teaching Exp, ANUniv, Authored 35 Books, Published 65 Research Papers (Algebra/Fuzzy Algebra/Graph Theory) in International Journals. Dr Nagaraju Dasari, 3yr of Teaching Exp. in Univ, Published 10RP, Research Student of Dr Bhavanari for his Ph.D

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