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- simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero proper submodules. Equivalently, a module M...9 KB (1,345 words) - 04:22, 19 May 2025
- R-modules preserves exactness. Torsionless A module is called torsionless if it embeds into its algebraic dual. Simple A simple module S is a module that...22 KB (3,091 words) - 12:09, 26 March 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
- Indecomposable is a weaker notion than simple module (which is also sometimes called irreducible module): simple means "no proper submodule" N < M, while...5 KB (705 words) - 22:27, 28 October 2023
- Semi-simplicity (redirect from Completely-reducible module)trivial module 0 is semi-simple, but not simple). For an R-module M, M is semi-simple if and only if it is the direct sum of simple modules (the trivial...13 KB (1,867 words) - 10:13, 18 February 2024
- Composition series (category Module theory)structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that...9 KB (1,331 words) - 16:45, 28 December 2024
- as module theory, a principal indecomposable module has many important relations to the study of a ring's modules, especially its simple modules, projective...4 KB (501 words) - 15:49, 7 April 2020
- R-module N is cyclic if N = yR for some y ∈ N. 2Z as a Z-module is a cyclic module. In fact, every cyclic group is a cyclic Z-module. Every simple R-module...3 KB (404 words) - 00:12, 27 April 2024
The Apollo command and service module (CSM) was one of two principal components of the United States Apollo spacecraft, used for the Apollo program, which...74 KB (7,757 words) - 16:17, 7 June 2025
Solar panel (redirect from Solar module)panels are also known as solar cell panels, solar electric panels, or PV modules. Solar panels are usually arranged in groups called arrays or systems....82 KB (9,283 words) - 14:58, 30 May 2025
led to the creation of the Whitehead manifold. The definition of crossed modules is due to him. He also made important contributions in differential topology...9 KB (862 words) - 18:30, 4 April 2025- algebra, an Artinian module is a module that satisfies the descending chain condition on its poset of submodules. They are for modules what Artinian rings...8 KB (1,115 words) - 23:54, 13 May 2025
- mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field...4 KB (492 words) - 21:04, 25 April 2025
- example, a semisimple module is a module that has a decomposition into simple modules. Given a ring, the types of decomposition of modules over the ring can...15 KB (2,681 words) - 16:58, 23 January 2024
- abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers...28 KB (3,919 words) - 09:32, 15 February 2025
- A/0 Modules/Async/A Modules/AsynchronousDefinition Modules/LoaderPlugin Modules/Resources Modules/SimpleAsynchronous Modules/Transport/B,C,D,E Modules/Wrappings...10 KB (956 words) - 15:25, 11 June 2024
- Weight (representation theory) (redirect from Simple highest weight module)isomorphism) simple highest-weight g {\displaystyle {\mathfrak {g}}} -module with highest weight λ, which is denoted L(λ), but this module is infinite...22 KB (3,368 words) - 17:09, 14 April 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
- Modular representation theory (category Module theory)the number of simple modules k(G) is equal to the number of conjugacy classes of G. In the modular case, the number l(G) of simple modules is equal to the...18 KB (2,613 words) - 08:46, 23 November 2024
- and the vector space M = N is a simple module of R. Then Schur's lemma says that the endomorphism ring of the module M is a division algebra over k. If...23 KB (3,820 words) - 03:30, 29 April 2025
- Mya kowd, an echo Module:Wikt error: no link provided, to-morrow, Module:Wikt error: no link provided, the day before yesterday Module:Wikt error: no link
- Tranquility Base here. The Eagle has landed. First words from the Apollo 11 lunar module Eagle after guiding the craft to a landing on the Moon at 4:17pm EDT (20
- and modules is case sensitive, therefore test() and TEST() refer to different functions/modules. Modules and functions can be defined within a module definition