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...

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...

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

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...

"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...

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...

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...

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...

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...

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...

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) =...

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...