Examples of 'commutative ring' in a sentence
Meaning of "commutative ring"
commutative ring: In mathematics, this phrase describes a type of algebraic structure characterized by two binary operations, addition and multiplication, which satisfy commutativity. It means that the order in which elements are combined under addition or multiplication does not affect the final result
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- A ring whose multiplicative operation is commutative.
How to use "commutative ring" in a sentence
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commutative ring
A commutative ring is a ring whose multiplication is commutative.
Moduli spaces of commutative ring spectra.
A commutative ring is a ring where multiplication is commutative.
Relationship to other commutative ring classes.
A commutative ring is left primitive if and only if it is a field.
Fix a partition λ of n and a commutative ring k.
Every countable commutative ring has a prime ideal.
Signatures of higher level on a commutative ring.
Every countable commutative ring has a maximal ideal.
Strongly irreducible ideals of a commutative ring.
A commutative ring is a prime ring if and only if it is an integral domain.
Tensor product of two modules over a commutative ring.
Any commutative ring is the colimit of finitely generated subrings.
Algebra over a commutative ring.
It can be proven with elementary algebra and holds in every commutative ring.
See also
Is a commutative ring.
An example is the category of projective modules over a commutative ring.
The ring is called a commutative ring if it also has commutativity under multiplication.
These edge weights are assumed to belong to some commutative ring.
The structure of a noncommutative ring is more complicated than that of a commutative ring.
It is easy to prove that the identity holds in any commutative ring.
A commutative algebra over a commutative ring is called a reduced algebra if its underlying ring is reduced.
Let us define the modules and algebras on a unitary commutative ring.
Let R be a commutative ring and n a natural number.
These germs can be added and multiplied and form a commutative ring.
We assume that R is a commutative ring with unity.
A commutative monoid in the category of simplicial abelian groups is a simplicial commutative ring.
Any module over a commutative ring R is automatically a bimodule.
The discriminant can even be defined for polynomials over any commutative ring.
We assume that R is a commutative ring with identity element.
The formula is valid for matrices with the entries from any commutative ring.
Let R be a commutative ring of prime characteristic p.
Let A be a unital algebra over a commutative ring k.
Let R be a fixed commutative ring so R could be a field.
Throughout this chapter we shall assume that R is a commutative ring.
In a commutative ring any ideal must be two-sided.
This statement generalizes only to the case where V and W are projective modules over a commutative ring.
Let C be a category and R be a commutative ring with unit.
In particular, a commutative ring is an integral domain if and only if is a prime ideal.
Let R be an effective commutative ring.
In particular, any commutative ring is an algebra over any of its subrings.
In general, such functions will form a commutative ring.
In a commutative ring with unity, every maximal ideal is a prime ideal.
Let A be a unitary commutative ring.
In a commutative ring the invertible elements, or units, form an abelian multiplicative group.
As the multiplication of integers is a commutative operation, this is a commutative ring.
A nonzero commutative ring whose only zero divisor is 0 is called an integral domain.
In other words, it is a ringed space which is locally a spectrum of a commutative ring.
Consequently, the singular ideal of a commutative ring contains the nilradical of the ring.
The real numbers can be extended to a wheel, as can any commutative ring.
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Examples of using Ring
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And place a ring upon her hand
Ring tones will not hold up in court
I had to go into the ring to finish it myself
Examples of using Commutative
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A commutative ring is a ring whose multiplication is commutative
This addition is both commutative and associative
Commutative rings are also important in algebraic geometry
