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What (who) is commutative ring - definition
Commutative ring
![The [[universal property]] of ''S'' ⊗<sub>''R''</sub> ''T''
states that for any two maps ''S'' → ''W'' and ''T'' → ''W'' which make the outer quadrangle commute, there is a unique map ''S'' ⊗<sub>''R''</sub> ''T'' → ''W'' which makes the entire diagram commute.](https://commons.wikimedia.org/wiki/Special:FilePath/Tensor product of algebras.png?width=200 "The [[universal property]] of ''S'' ⊗<sub>''R''</sub> ''T''
states that for any two maps ''S'' → ''W'' and ''T'' → ''W'' which make the outer quadrangle commute, there is a unique map ''S'' ⊗<sub>''R''</sub> ''T'' → ''W'' which makes the entire diagram commute.")
ALGEBRAIC STRUCTURE
Commutative rings; Cring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra.
Graded-commutative ring
(ℤ/2)-GRADED RING IN WHICH EVEN ELEMENTS COMMUTE AMONG THEMSELVES, ODD ELEMENTS ANTICOMMUTE AMONG THEMSELVES, AND EVEN AND ODD ELEMENTS COMMUTE
Graded-commutative; Skew-commutative ring
In algebra, a graded-commutative ring (also called a skew-commutative ring) is a graded ring that is commutative in the graded sense; that is, homogeneous elements x, y satisfy
Commutative ring spectrum
COMMUTATIVE MONOID IN A GOOD CATEGORY OF SPECTRA; ROUGHLY EQUIVALENT TO AN E∞-RING SPECTRUM
Commutative ring spectra; Good category of commutative ring spectra
In the mathematical field of algebraic topology, a commutative ring spectrum, roughly equivalent to a E_\infty-ring spectrum, is a commutative monoid in a goodsymmetric monoidal with respect to smash product and perhaps some other conditions; one choice is the category of symmetric spectra category of spectra.
