# Commutative Rings

### Some articles on rings, commutative rings, ring, commutative ring, commutative:

Areas Of Mathematics - Major Divisions of Mathematics - Algebra
... to solve equations leads to the field of abstract algebra, which, among other things, studies rings and fields, structures that generalize the ... Commutative rings and algebras In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the commutative law ... This means that if a and b are any elements of the ring, then a×b=b×a ...
Flat Module - Definition - Commutative Rings
... There are many ways to define flatness over a commutative ring ... A flat -module is an -module such that the functor is exact, where is the category of -modules ...
Nil Ideal - Commutative Rings
... In a commutative ring, the set of all nilpotent elements forms an ideal known as the nilradical of the ring ... Therefore, an ideal of a commutative ring is nil if, and only if, it is a subset of the nilradical that is, the nilradical is the ideal maximal with respect to the property that each of its ... In commutative rings, the nil ideals are more well-understood compared to the case of noncommutative rings ...
Nicolae Popescu - Original Articles and References
... On the localization ring of ring, J ... Some remarks about semi-Artinian rings, Rev ... Exemple de inele semi-artiniene, (Examples of semi-Artinian rings), Stud ...
Category Of Rings - Subcategories - Category of Commutative Rings
... The category of commutative rings, denoted CRing, is the full subcategory of Ring whose objects are all commutative rings ... is one of the central objects of study in the subject of commutative algebra ... Any ring can be made commutative by taking the quotient by the ideal generated by all elements of the form (xy − yx) ...

### Famous quotes containing the word rings:

The next time the novelist rings the bell I will not stir though the meeting-house burn down.
Henry David Thoreau (1817–1862)