Chapter 1 Rings Flashcards
1
Q
What is a Ring?
A
A RING is a set with two binary operations + and x that satisfy
(R1) is an abelian group with an identity O
(R2) x is associative
(R3) x is distributive over +
(R4) There exists an element I in R that is an identity for multiplication
2
Q
What is a subring?
A
Let R be a ring, S is a SUBRING of R if it is a ring in its own right with respect to + and x and I_R is within S
3
Q
What is the cartesian product of two rings?
A
If P and Q are rings then the CARTESIAN PRODUCT PxQ with operations + and x defined (P1, P2)+(Q1, Q2)=(P1+Q1, P2,+Q2) and (P1, P2)x(Q1, Q2)=(P1xQ1, P2,xQ2) is a ring. The element (0,0) is the zero of this ring and (1,1) is the one of this ring.
