Rings
An algebraic system <R, +, • >, where R is a non-empty set, ‘+’ and ‘•’ Two binary compositions defined onset R is called a ring if. (R, +) is Abelian group (a+b)+c = a+(b+c) for all a,b,c ∊ R a+b = b+a for all a,b ∊ R for all a ∊ R, - a ∊ R, such that a+(-a) = 0 for all a ∊ R, o ∊ R such that a + o = a (R, • ) is semi group (ab)c = a(bc) Distributev Law {a(b+c) = ab + ac} and {(a+b)c = ac + bc} for all a,b,c ∊ R Key Terms in Rings: - Integral Domain: - A commutative ring R which contains no proper zero-divisor is called an integral domain. If ab = 0 for a,b ∊ z then a = 0 or b = 0 Sub ring: - A non-empty subset S ...