Elementary Properties of Rings

Ernest Shult () and David Surowski
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Ernest Shult: Kansas State University, Department of Mathematics

Chapter Chapter 7 in Algebra, 2015, pp 185-230 from Springer

Abstract: Abstract Among the most basic concepts concerning rings are the poset of ideals (left, right and 2-sided), possible ring homomorphisms, and the group of units of the ring. Many examples of rings are presented—for example the monoid rings (which include group rings and polynomial rings of various kinds), matrix rings, quaternions, algebraic integers etc. This menagerie of rings provides a playground in which the student can explore the basic concepts (ideals, units, etc.) in vivo.

Keywords: Commutative Ring; Identity Element; Integral Domain; Polynomial Ring; Left Ideal (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-19734-0_7

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