Length of a module

In abstract algebra, the length of a module is a generalization of the dimension of a vector space which measures its size. page 153 In particular, as in the case of vector spaces, the only modules of finite length are finitely generated modules. It is defined to be the length of the longest chain of submodules. Modules with finite length share many important properties with finite-dimensional vector spaces. Other concepts used to 'count' in ring and module theory are depth and height; these are both somewhat more subtle to define.

Tianhe core module
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Tianhe core module ... Tiānhé; lit. 'Harmony of the Heavens'), also known as the Tianhe core module (Chinese: 天和号核心舱), is the first module to launch of the Tiangong space station...

Shenzhou (spacecraft)
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Shenzhou (spacecraft) ... modules return, and the Shenzhou 5 orbital module continued to operate for six months after launch. Orbital module data Design life: 200 days Length:...

Injective module
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Injective module ... area of 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...

Simple module
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Simple module ... submodule generated by a non-zero element of M equals M. Simple modules form building blocks for the modules of finite length, and they are analogous...

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

Dimension (vector space)
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Dimension (vector space) ... can see a vector space as a particular case of a matroid, and in the latter there is a well-defined notion of dimension. The length of a module and the...

M.2
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M.2 ... Employing a more flexible physical specification, the M.2 allows different module widths and lengths, and, paired with the availability of more advanced...

Soyuz (spacecraft)
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Soyuz (spacecraft) ... front to back): A spheroid orbital module, which provides accommodation for the crew during their mission; A small aerodynamic reentry module, which returns...

Flat module
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Flat module ... algebra, a flat module over a ring R is an R-module M such that taking the tensor product over R with M preserves exact sequences. A module is faithfully...

Homological conjectures in commutative algebra
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Homological conjectures in commutative algebra ... denote a finite complex of free R-modules such that ⨁ i H i ( G ∙ ) {\displaystyle \bigoplus \nolimits _{i}H_{i}(G_{\bullet })} has finite length but is...

Sri Krishna 2006
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