Answer to Question #47345 in Abstract Algebra for ayush kumar

Question

(a) Show that a permutation is even if and only 4 if its signature is + 1. Find the signature of (2 3 4) E S4 using the definition of signature.

(b) Show that, in a finite commutative ring, 6 every non-zero element is either a zero divisor or a unit. Also find the number of zero divisors of Z20.