Search results with tag "Ring theory"
Mathematics Course 111: Algebra I Part III: Rings ...
www.maths.tcd.ieIdeals play a role in ring theory analogous to the role of normal subgroups in group theory. Example. Let Z be the ring of integers and, for any non-negative integer n, let nZ be the subset of Z consisting of those integers that are multiples of n. Then nZ is an ideal of Z. Proposition 7.4. Every ideal of the ring Z of integers is generated by ...
RING THEORY 1. Ring Theory - Northwestern University
sites.math.northwestern.edu32 IV. RING THEORY If A is a ring, a subset B of A is called a subring if it is a subgroup under addition, closed under multiplication, and contains the identity. (If A or B does not have an identity, the third requirement would be dropped.) Examples: 1) Z does not have any proper subrings. 2) The set of all diagonal matrices is a subring ofM n(F). 3) The set of all n by n matrices which …
Ring Theory (Math 113), Summer 2014
math.berkeley.eduRing Theory (Math 113), Summer 2014 James McIvor University of California, Berkeley August 3, 2014 Abstract These are some informal notes on rings and elds, used to teach Math 113 at UC Berkeley, Summer 2014. We go through the basic stu : …