Rings and domains

Concepts

• Unit of a ring 10 exercisesA unit of a ring R with identity 1 is an element u that has a multiplicative inverse v within R.
• Zero divisor 10 exercisesA zero divisor of a ring R is an element a≠0 for which there is another element b≠0 of R whose product with a is zero.
• Characteristic of a ring 10 exercisesThe characteristic of a ring R with identity 1 is the least positive integer n such that adding the identity to itself n times gi…
• First isomorphism theorem for rings 10 exercisesIf φcolon R→ S is a ring homomorphism with kernel kerφ, the quotient ring of R by kerφ is isomorphic to the image of φ.