finite-dimensional ring
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Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… … Wikipedia
Finite projective geometry — In mathematics, a finite projective space S is a set P (the set of points), together with a set of subsets of P (the set of lines), all of which have at least three elements, satisfying these axioms : * Each two distinct points p and q are in… … Wikipedia
Division ring — In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a non trivial ring in which every non zero element a has a multiplicative inverse, i.e., an element x with a·x = x·a = 1 … Wikipedia
Commutative ring — 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. Some specific kinds of commutative rings are given with … Wikipedia
Primitive ring — In mathematics, especially in the area of abstract algebra known as ring theory, the concept of left primitive ring generalizes that of matrix algebra. Every matrix ring is the endomorphism ring of a finite dimensional vector space, but a… … Wikipedia
Endomorphism ring — In abstract algebra, one associates to certain objects a ring, the object s endomorphism ring, which encodes several internal properties of the object. We will start with the example of abelian groups. Suppose A is an abelian group. As the name… … Wikipedia
Burnside ring — In mathematics, the Burnside ring of a finite group is an algebraic construction that encodes the different ways the group can act on finite sets. The ideas were introduced by William Burnside at the end of the nineteenth Century, but the… … Wikipedia
Representation ring — In mathematics, especially in the area of algebra known as representation theory, the representation ring of a group is a ring formed from all the (isomorphism classes of the) linear representations of the group. For a given group, the ring will… … Wikipedia
Artinian ring — In abstract algebra, an Artinian ring is a ring that satisfies the descending chain condition on ideals. They are also called Artin rings.There are two classes of rings that have very similar properties:* Rings whose underlying sets are finite. * … Wikipedia
Simple ring — In abstract algebra, a simple ring is a non zero ring that has no ideal besides the zero ideal and itself. A simple ring can always be considered as a simple algebra.According to the Artin Wedderburn theorem, every simple ring that is left or… … Wikipedia
Order (ring theory) — In mathematics, an order in the sense of ring theory is a subring of a ring R that satisfies the conditions R is a ring which is a finite dimensional algebra over the rational number field spans R over , so that … Wikipedia
