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- 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...4 KB (543 words) - 07:45, 16 December 2024
- (mathematics) Quotient category Quotient graph Integer division Quotient module Quotient object Quotient of a formal language, also left and right quotient Quotient...8 KB (825 words) - 05:19, 31 January 2025
- 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...22 KB (3,091 words) - 12:09, 26 March 2025
- 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...9 KB (1,345 words) - 04:22, 19 May 2025
- Equivalence class (redirect from Quotient set)abstract algebra, the term quotient space may be used for quotient modules, quotient rings, quotient groups, or any quotient algebra. However, the use...17 KB (2,417 words) - 17:27, 23 May 2025
- 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...28 KB (3,919 words) - 09:32, 15 February 2025
- Localization (commutative algebra) (redirect from Ring of quotients)"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...30 KB (5,381 words) - 12:29, 1 June 2025
- 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...10 KB (1,249 words) - 15:50, 18 September 2024
- 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...11 KB (1,567 words) - 15:45, 28 December 2024
- 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...18 KB (3,363 words) - 21:03, 1 April 2025
- 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...20 KB (2,878 words) - 01:09, 6 May 2025
- semisimple Lie algebra. Specifically, although Verma modules themselves are infinite dimensional, quotients of them can be used to construct finite-dimensional...24 KB (4,330 words) - 21:36, 5 October 2024
- List of abstract algebra topics (section Module theory)Direct limit Direct product Inverse limit Quotient objects: quotient group, quotient ring, quotient module etc. Tensor product Advanced concepts: Category...12 KB (1,129 words) - 10:50, 10 October 2024
- 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...17 KB (2,958 words) - 21:08, 21 January 2025
- Ring (mathematics) (section Quotient 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...99 KB (13,738 words) - 11:06, 29 May 2025
- 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...14 KB (2,467 words) - 20:36, 5 March 2025
- 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) =...5 KB (596 words) - 04:53, 6 January 2023
- 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...15 KB (2,160 words) - 10:01, 5 March 2025
- 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...23 KB (3,081 words) - 01:20, 19 May 2025
- 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...8 KB (1,115 words) - 23:54, 13 May 2025
- expressed in feet or inches, by the number of modules belonging to the order, and the quotient will be the module or semidiameter of the base of the col- umn
- Definition (quotient topological module): Let M {\displaystyle M} be a topological module over the topological ring R {\displaystyle R} , and let N ≤