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  2. Module (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Module_(mathematics)

    A module is called flat if taking the tensor product of it with any exact sequence of 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 is not {0} and whose only submodules are {0} and S. Simple modules are sometimes called irreducible. [5 ...

  3. Simple module - Wikipedia

    en.wikipedia.org/wiki/Simple_module

    Z-modules are the same as abelian groups, so a simple Z-module is an abelian group which has no non-zero proper subgroups.These are the cyclic groups of prime order.. If I is a right ideal of R, then I is simple as a right module if and only if I is a minimal non-zero right ideal: If M is a non-zero proper submodule of I, then it is also a right ideal, so I is not minimal.

  4. Computer module - Wikipedia

    en.wikipedia.org/wiki/Computer_module

    A computer module is a selection of independent electronic circuits packaged onto a circuit board to provide a basic function within a computer. [1] An example might be an inverter or flip-flop , which would require two or more transistors and a small number of additional supporting devices.

  5. Glossary of module theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_module_theory

    A module of finite length is a module that admits a (finite) composition series. finite presentation 1. A finite free presentation of a module M is an exact sequence where are finitely generated free modules. 2.

  6. Semisimple module - Wikipedia

    en.wikipedia.org/wiki/Semisimple_module

    The most basic example of a semisimple module is a module over a field, i.e., a vector space. On the other hand, the ring Z of integers is not a semisimple module over itself, since the submodule 2Z is not a direct summand. Semisimple is stronger than completely decomposable, which is a direct sum of indecomposable submodules.

  7. Structure chart - Wikipedia

    en.wikipedia.org/wiki/Structure_Chart

    number of readily identifiable functions and modules within each function and; whether each identifiable function is a manageable entity or should be broken down into smaller components. A structure chart is also used to diagram associated elements that comprise a run stream or thread.

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  9. Decomposition of a module - Wikipedia

    en.wikipedia.org/wiki/Decomposition_of_a_module

    Since a simple module is indecomposable, a semisimple decomposition is an indecomposable decomposition (but not conversely). If the endomorphism ring of a module is local, then, in particular, it cannot have a nontrivial idempotent: the module is indecomposable. Thus, a decomposition with local endomorphism rings is an indecomposable decomposition.