Preliminaries and Basic Results

Gary F. Birkenmeier, Jae Keol Park and S. Tariq Rizvi
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Gary F. Birkenmeier: University of Louisiana at Lafayette, Department of Mathematics
Jae Keol Park: Busan National University, Department of Mathematics
S. Tariq Rizvi: The Ohio State University at Lima, Department of Mathematics

Chapter Chapter 1 in Extensions of Rings and Modules, 2013, pp 1-17 from Springer

Abstract: Abstract In this beginning chapter of the book, basic notions, definitions, terminology, and notations used throughout the book are presented. Preliminary results and related material have been included for the convenience of the reader.

Keywords: Fully invariant submodule; Closed submodule; Faithful module; (Second) singular submodule; Right nonsingular; Regular ring; Abelian; Right (semi)hereditary; Semiprimary; Uniform dimension; Set of matrix units; Classical right ring of quotients; Semicentral idempotent; Semicentral reduced; I-ring; (Strongly) π-regular; Bounded index (of nilpotency); Rational extension; Quasi-Frobenius (QF); Dense submodule; Rational hull; (Maximal) right ring of quotients; Martindale right ring of quotients; Symmetric ring of quotients; Right Kasch (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-0-387-92716-9_1

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