$#C+1 = 98 : ~/encyclopedia/old_files/data/D031/D.0301210 Derivation in a ring
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is the ring of integers in the imaginary quadratic number field $ \mathbf Q ( \sqrt {
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...he characteristic property of an imbedding of a group (ring) into a group (ring) as a normal subgroup (ideal). Let $\mathfrak{K}$ be a [[Category|category]
...$H$. However, in an additive category the concepts of normal monomorphism and regular monomorphism coincide.
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the completion of $k$ with respect to $\nu\in V$, and $O_\nu$ is the
ring of integer elements in $k_\nu$. The adèle group of an algebraic
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...all png images have been replaced by TeX code, please remove this message and the {{TEX|semi-auto}} category.
...igma$ of $R$ extends uniquely to an automorphism $\hat { \sigma }$ of $Q$, and one says that $\sigma$ is $X$-inner if $\hat { \sigma }$ is inner on $Q$ (c
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A characteristic class defining a ring homomorphism $ \mathop{\rm ch} : K ( X) \rightarrow H ^ {**} ( X ; \m
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...y subgroup of finite index in $\def\O{\mathcal{O}}G_\O$, where $\O$ is the ring of integers in an algebraic number field $k$ (cf.
[[Algebraic number theory|Algebraic number theory]]) and $G$ is a connected
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''Associative rings and algebras'' are
rings and algebras with an associative multiplication, i.e., sets with
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A [[Prime ideal|prime ideal]] in a [[Dedekind ring|Dedekind ring]] $ A $
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...bf{Z}_p$ of $p$-adic integers is a pro-$p$-group. In Galois theory pro-$p$-groups appear as [[Galois group]]s of $p$-extensions of fields.
...roperties: 1) $G$ is the smallest closed subgroup of $G$ generated by $E$; and 2) any neighbourhood of the identity of $G$ contains almost-all (i.e. all e
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over the integral group ring $ \mathbf Z [ H ] $(
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Algebras introduced by B.Yu. Weisfeiler and A.A. Leman [[#References|[a9]]] and initially studied by representatives of the Soviet school of algebraic comb
A cellular algebra $W$ of order $n$ and rank $r$ is a matrix subalgebra of the full matrix algebra $\mathbf{C}^{n \
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[[Category:Number theory]]
An idele (also: idèle) is an invertible element of the ring of
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...e ring $R$ that is a topological space in which the operations of addition and multiplication, as well as the mapping $R\times A\to A$ ($(r,a)\to ra$), ar
...ctures, i.e. groups, semi-groups, rings, lattices, vector spaces, modules, and others, equipped with topologies in which the algebraic operations consider
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and $ U _ {t} $
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$#C+1 = 44 : ~/encyclopedia/old_files/data/R082/R.0802430 Ring with divided powers
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...encyclopedia/old_files/data/R081/R.0801470 Representation of the symmetric groups
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...r]] from $\Gamma$ to the [[category]] of $R$-modules, for some commutative ring $R$ (cf. also [[Module]]). Taking morphisms to be natural transformations,
...orbits $G/H$ and $G$-mappings between them. $\mathbf{Z}$-modules (Abelian groups) over $\mathcal{O}_G$ play the role of the coefficients in Bredon's ($\math
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...n, i.e. to use the plus sign ($+$) for that operation, called "addition", and the zero sign for the neutral element, named zero (in multiplicative notati
...a group in which all finitely generated subgroups are cyclic. Finally, the groups of type $p^\infty$ (or the [[quasi-cyclic group]]s $\mathbf Z_{p^\infty}$),
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and $ x + \infty = \infty + x = \infty $
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