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Show that the nilpotent elements of a commutative ring
Chapter 13, Problem 16E(choose chapter or problem)
Problem 16E
Show that the nilpotent elements of a commutative ring form a subring.
Questions & Answers
QUESTION:
Problem 16E
Show that the nilpotent elements of a commutative ring form a subring.
ANSWER:
Step 1 of 6
A ring R is a set with two binary operations such as addition and multiplication that satisfies several properties.
R is an Abelian group under addition and multiplication operation satisfies the associative law.
According to distributive laws
For every
This identity of the addition operation is denoted 0. If the multiplication operation has an identity it is called a unity. If multiplication is commutative we say that R is commutative.
A subring of a ring R is a subset
That is a ring under the operations of R.
Let a be an element of a ring R. The element a is a nilpotent if and only if there exists a positive integer 
