Recent content by dndod1

Homework Statement This is not an assignment question, just something that I am wondering about as an offshoot of an assignment question. In my course notes Rings are defined as having 3 axioms and commutative rings have 4.(outined below) I have just answered this question: Show that the...

Thanks very much for getting me started. I have shown that the function is 1-1 and that it is onto. I still do not know how to tackle the last part of question a), as I am confused by the lambda notation. Thus show that there is an element ea for each a, such that lambda a(ea)=a. My...

Homework Statement Let S be a finite multiplicative semigroup in which these 2 cancellation laws hold. For all a,x,y \in S, a*x=a*y implies x=y and for all a,x,y, \in S x*a=y*a implies that x=y. Show that (S, *) is a group. For given a \in S, let \lambda a: S \rightarrow S, s...

Thanks for that. I shall give it another go. If I don't relate the sets in part b to what I showed in part a, am I not ignoring the part of the question that says "Use the equivalence from part a"?

Homework Statement Part a: Show that X \subseteq Y and X \subseteq Z if and only if X\subseteq Y \cap Z, for sets X,Y,Z. I have done this. Part b: Use the equivalence from part a to establish the identity P(A) \cap P(B)= P(A \cap B), where P is the power set. Homework Equations...

Thank you very much for your help. Much appreciated!

Homework Statement A relation p is defined on R^2 (fancy R, as in Reals) by (a,b)p (c,d) if a+d=b+c Show that p is an equivalence relation. b) Consider R^2 to be the Cartesian Plane. Describe p's equivalence classes geometrically. (Consider which points will be in the particular...

Thank you! I shall alter my notation. Much appreciated!

Thank you Dick. I got there! Thank you for your extremely quick reply. I really appreciate your help. Many thanks.

Homework Statement Using only the ring axioms, prove that in a general ring (R, +,X) aX (x-z) = (aXx)- (aXz) where all a,x,z are elements of R Homework Equations Group axiom 3: G3= There is an inverse for each element g^-1 *g =e Ring axiom 3: R3= Two distributive laws...