Search results

given a module and a submodule, one can construct their quotient module. This construction, described below, is very similar to that of a quotient vector...

(mathematics) Quotient category Quotient graph Integer division Quotient module Quotient object Quotient of a formal language, also left and right quotient Quotient...

abstract algebra, the term quotient space may be used for quotient modules, quotient rings, quotient groups, or any quotient algebra. However, the use...

ideals and quotient rings are modules, so that many arguments about ideals or quotient rings can be combined into a single argument about modules. In non-commutative...

is isomorphic to a quotient R/m where m is a maximal right ideal of R. By the above paragraph, any quotient R/m is a simple module. Conversely, suppose...

the R-module K is an injective R-module, and indeed the smallest injective R-module containing R. For any Dedekind domain, the quotient module K/R is...

area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from...

"denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/module R, so that it consists of fractions...

quotient topology. If, furthermore, X is metrizable, then so is X/M. If X is a Fréchet space, then so is X/M. Quotient group Quotient module Quotient...

mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of...

M} for some n; in other words, M is a quotient of a free module of finite rank. If a set S generates a module that is finitely generated, then there...

semisimple Lie algebra. Specifically, although Verma modules themselves are infinite dimensional, quotients of them can be used to construct finite-dimensional...

algebra, a module homomorphism is a function between modules that preserves the module structures. Explicitly, if M and N are left modules over a ring...

module over a semisimple ring is semisimple. (Proof: A free module over a semisimple ring is semisimple and any module is a quotient of a free module...

Herbrand module is an A for which the cohomology groups are finite. In this case, the Herbrand quotient h(G,A) is defined to be the quotient h(G,A) =...

Direct limit Direct product Inverse limit Quotient objects: quotient group, quotient ring, quotient module etc. Tensor product Advanced concepts: Category...

algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group...

for a finitely generated module over R might not exist. However such a module is still isomorphic to a quotient of some module Rn with n finite (to see...

projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, keeping some of the main properties of free modules. Various...

Noetherian modules, Artinian modules enjoy the following heredity property: If M is an Artinian R-module, then so is any submodule and any quotient of M. The...