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Module homomorphism - Wikipedia

https://en.wikipedia.org/wiki/Module_homomorphism
Note: the above verification would "fail" if one used the left R-action in place of the right S-action

Embedding - Wikipedia

https://en.wikipedia.org/wiki/Embedding
[3] More explicitly, an injective continuous map f : X → Y {\displaystyle f:X\to Y} between topological spaces X {\displaystyle X} and Y {\displaystyle Y} is a topological embedding if f {\displaystyle f} yields a homeomorphism between X {\displaystyle X} and f ( X ) {\displaystyle f(X)} (where f ( X ) {\displaystyle

Ideal (ring theory) - Wikipedia

https://en.wikipedia.org/wiki/Ideal_(ring_theory)
An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group

Noncommutative ring - Wikipedia

https://en.wikipedia.org/wiki/Noncommutative_ring
x n ⟩ / ( x i x j − q i j x j x i ) {\displaystyle \mathbb {C} \langle x_{1},\ldots ,x_{n}\rangle /(x_{i}x_{j}-q_{ij}x_{j}x_{i})} , called a quantum plane, where q i j ∈ C {\displaystyle q_{ij}\in \mathbb {C} } Any Clifford algebra can be described explicitly using an algebra presentation: given an F {\

Semigroup - Wikipedia

https://en.wikipedia.org/wiki/Semigroup
If the semigroup operation is commutative, then the semigroup is called a commutative semigroup or (less often than in the analogous case of groups) it may be called an abelian semigroup

Group (mathematics) - Wikipedia

https://en.wikipedia.org/wiki/Group_(mathematics)
In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory

Financial economics - Wikipedia

https://en.wikipedia.org/wiki/Financial_economics
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Operator algebra - Wikipedia

https://en.wikipedia.org/wiki/Operator_algebra
From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator

Glossary of commutative algebra - Wikipedia

https://en.wikipedia.org/wiki/Glossary_of_commutative_algebra
  An ideal in a polynomial ring over a field is called absolutely prime if its extension remains prime for every extension of the field

List of abstract algebra topics - Wikipedia

https://en.wikipedia.org/wiki/List_of_abstract_algebra_topics
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Shing-Tung Yau - Wikipedia

https://en.wikipedia.org/wiki/Shing-Tung_Yau
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Double centralizer theorem - Wikipedia

https://en.wikipedia.org/wiki/Double_centralizer_theorem
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Up to - Wikipedia

https://en.wikipedia.org/wiki/Up_to
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Wedderburn–Artin theorem - Wikipedia

https://en.wikipedia.org/wiki/Wedderburn%E2%80%93Artin_theorem
} Here we used right modules because R ≅ E n d ( R R ) {\displaystyle R\cong \mathrm {End} (R_{R})} ; if we used left modules R {\displaystyle R} would be isomorphic to the opposite algebra of E n d ( R R ) {\displaystyle \mathrm {End} ({}_{R}R)} , but the proof would still go through

Outline of category theory - Wikipedia

https://en.wikipedia.org/wiki/Outline_of_category_theory
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Ideal norm - Wikipedia

https://en.wikipedia.org/wiki/Ideal_norm
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Conjugate diameters - Wikipedia

https://en.wikipedia.org/wiki/Conjugate_diameters
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Invariant basis number - Wikipedia

https://en.wikipedia.org/wiki/Invariant_basis_number
Assuming the ultrafilter lemma (a strictly weaker form of the axiom of choice), this result is actually equivalent to the definition given here, and can be taken as an alternative definition

Bali myna - Wikipedia

https://en.wikipedia.org/wiki/Bali_myna
[1] In 2018, there were three locations on Bali where the birds existed in the wild: the West Bali National Park; Bali's small island of Nusa Penida and Begawan Foundation's breeding and release site at Melinggih Kelod, Payangan

Dobiński's formula - Wikipedia

https://en.wikipedia.org/wiki/Dobinski's_formula
[3] Recall that if x {\displaystyle x} and n {\displaystyle n} are nonnegative integers then the number of one-to-one functions that map a size- n {\displaystyle n} set into a size- x {\displaystyle x} set is the falling factorial ( x ) n = x ( x − 1 ) ( x − 2 ) ⋯ ( x − n + 1 ) {\displaystyle (x)_{n}=x(x-1)(x-2

Gentoo Linux - Wikipedia

https://en.wikipedia.org/wiki/Gentoo_Linux
-- Weekly minimal install builds are available on Gentoo's site above the old 2008 releases -->"},"latest release date":{"wt":

Artificial intelligence - Wikipedia

https://en.wikipedia.org/wiki/Artificial_intelligence
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Krull's theorem - Wikipedia

https://en.wikipedia.org/wiki/Krull's_theorem
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Formal power series - Wikipedia

https://en.wikipedia.org/wiki/Formal_power_series_ring
} If we studied this as a power series, its properties would include, for example, that its radius of convergence is 1 by the Cauchy–Hadamard theorem

Lithium–sulfur battery - Wikipedia

https://en.wikipedia.org/wiki/Lithium%E2%80%93sulfur_battery
These constraints are interdependent: increasing sulfur loading or lowering E/S improves projected energy density, but can also increase polarization and lower reversible capacity if ion/electron transport and interfacial stability are not maintained

Grammatical gender

https://en.wikipedia.org/wiki/Grammatical_gender
Because of this, languages with gender distinction can often use pronouns where in English a noun would have to be repeated in order to avoid confusion

MS-DOS

https://en.wikipedia.org/wiki/MS-DOS
com/resources/documentation/windows/xp/all/proddocs/en-us/windows_dos_overview

Tragedy of the commons - Wikipedia

https://en.wikipedia.org/wiki/Tragedy_of_the_commons
He postulated that if a herder put more than his allotted number of cattle on the common, overgrazing could result

Nicolaus Copernicus - Wikipedia

https://en.wikipedia.org/wiki/Nicolaus_Copernicus
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Shell (computing)

https://en.wikipedia.org/wiki/Shell_(computing)
In the lower right we can see a terminal emulator running a Unix shell, in which the user can type commands as if they were sitting at a terminal