''left topological module''
...lian topological group can be given the natural structure of a topological module over the completion $\hat R$ of the ring $R$.
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...clopediaofmath.org/legacyimages/c/c025/c025920/c0259201.png" /> of a right
module <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
...//www.encyclopediaofmath.org/legacyimages/c/c025/c025920/c02592016.png" />-
module <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
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...ry decomposition. Any module of finite type over a Lasker ring is a Lasker module. E. Lasker [[#References|[1]]] proved that there is a primary decomposition
...R><TD valign="top">[3]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Commutative algebra" , Addison-Wesley (1972) (Translated from French)</T
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...the discipline is the notion of skein module, i.e., the quotient of a free module over ambient isotopy classes of links in a manifold by properly chosen loca
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...l prime ideals $(p)$, where $p$ divides the order of $M$. For an arbitrary module $M$ the set $\mathrm{Supp}(M)$ is empty if and only if $M=0$.
<TR><TD valign="top">[1]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Commutative algebra" , Addison-Wesley (1972) (Translated from French)</T
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[[Module|module]] $M$ into a (left) module $N$ over the same ring $A$, satisfying the conditions
...$ is also known as an anti-linear mapping. A semi-linear mapping of an $A$-module $M$ into itself is known as a semi-linear transformation.
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...the ring $A$ such that $\sum_{i\in I} a_i m_i = 0$. Thus there arises the module of syzygies, the chain complex of syzygies, etc. See also [[Hilbert syzygy
...gular algebras and regular sequences, cf. [[Koszul complex]]; [[Depth of a module]].
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$#C+1 = 38 : ~/encyclopedia/old_files/data/A010/A.0100860 Adjoint module,
''contragradient module, dual module''
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...free module by a submodule which is an image of a finitely-generated free module. Such a ring is called a left coherent ring; a right coherent ring is defin
module is finitely presentable; 2) a direct product of flat right $ R $-
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...e topology is said to be left linear). Similarly, a topology on a left $A$-module $E$ is linear if there is a fundamental system of neighbourhoods of zero co
...E'$, where $x\in E$ and $E'$ is a submodule of $E$) has a limit point. Any module of finite type over a complete local Noetherian ring is linearly compact.
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$#C+1 = 28 : ~/encyclopedia/old_files/data/F040/F.0400150 Filtered module
A module $ M $
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...s the conductor is regarded as an ideal of $\bar A$. If $\bar A$ is an $A$-module of finite type (e.g., if $A$ is a [[geometric ring]]), a [[prime ideal]] $\
<TR><TD valign="top">[1]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Commutative algebra" , Addison-Wesley (1972) (Translated from French)</T
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$#C+1 = 18 : ~/encyclopedia/old_files/data/I052/I.0502490 Invertible module
A [[module]] $M$ over a [[commutative ring]] $A$
2 KB (308 words) - 18:37, 11 April 2023
...ciative ring $A$ with unit is the algebra $T(V)$ over $A$ whose underlying module has the form
If the module $V$ is free and finitely generated, then $T(V^*)$ is naturally isomorphic t
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module $ M $
module.
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''of a module''
...n be represented as a direct sum of simple modules. [[Completely-reducible module]]s (semi-simple modules) can be characterized as modules that coincide with
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module $ E $''
module $ L _ {n} ( E, A) $,
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...e $E_1$ of the [[injective hull]] $E$ of the module $M/N$ (cf. [[Injective module]]) the intersection of the kernels of the homomorphisms from $E$ into $E_1$
<TR><TD valign="top">[1]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Commutative algebra" , Addison-Wesley (1972) (Translated from French)</T
3 KB (455 words) - 19:51, 5 October 2017
''of a left module $M$ over a ring $R$''
...$. In contrast to the dual notion of an injective envelope (an [[injective module]] $Q$ together with an essential monomorphism $M \rightarrow Q$) projective
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''of a module $M$''
...Anderson, K.R. Fuller, "Rings and Categories of Modules" Graduate Texts in Mathematics '''13''' Springer (2012) {{ISBN|1468499130}}
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