Commutative Algebra: Comprehensive Explanation

College
Algebra
Commutative Algebra

List all zero-divisors in $Z_{20}$ . Can you see relationship between the zero-divisors of $Z_{20}$ and the units of $Z_{20}$ ?

emancipezN 2020-11-29

Give an example of a commutative ring without zero-divisors that is not an integral domain.

Maiclubk 2020-11-27

Let R be a commutative ring. If I and P are idelas of R with P prime such that $I! \subseteq P$ , prove that the ideal $P : I = P$

Trent Carpenter 2020-11-23

If R is a commutative ring, show that the characteristic of R[x] is the same as the characteristic of R.

Dillard 2020-11-14

Prove the commutative properties of the convolution integral f * g = g * f

sagnuhh 2020-11-08

All idempotent elements in a commutative H ring with a characteristic 2 Check if they are creating a sub-ring. ( $a \in H$ idempotent $\Leftrightarrow a^{2} = a$ )

lwfrgin 2020-11-08

Assume that ab is a zero-divisor and that a and b are members of a commutative ring. A or B should be demonstrated to be zero-divisors.

emancipezN 2020-11-02

Let R be a commutative ring with identity and let I be a proper ideal of R. proe that $\frac{R}{I}$ is a commutative ring with identity.

Cabiolab 2020-10-27

True or False:
For $n \times n$ matrices A and B, define $A \otimes B = A B - B A$ . The operator ox is not associative or commutative.

nicekikah 2020-10-20

Let $A = {a, b, c, d}$
1. Find all combinatorial lines in $A^{2}$ . How many combinatorial lines are there?
2. Let n in $N$ . Prove that the number of combinatorial lines in $A^{n}$ equals $5^{n} - 4^{n}$

Annette Arroyo 2020-10-20

If a is an idempotent in a commutative ring, show that $1 - a$ is also an idempotent.

foass77W 2020-10-19

If a ring has the characteristic that, then prove that it is commutative ab = ca implies b = c when $a \neq 0$ .

In basic terms, commutative algebra represents a complex study of the rings that take place in algebraic number theory. It also relates to solving problems and questions based on algebraic geometry. You will see that there are solutions related to Dedekind rings and various commutative patterns. Commutative algebra solutions will be quite short in most cases, yet one should start with examples that are represented and link them with various questions. Take your time to post your commutative algebra example problem as well and always compare your question to similar questions as it will help you provide the required data. When you are dealing with inequality and graph solution tasks as you are seeking commutative equ

Commutative Algebra

Commutative Algebra Explained: In-Depth Examples, Equations, and Expert Insights