special notations in algebra

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$[G\!:\!H]$ , index (http://planetmath.org/Coset) of a subgroup $H$ in the group $G$
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$H\triangleleft G$ , $H$ is a normal subgroup of $G$
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$G/H$ , quotient group of $G$ with respect to the normal subgroup $H$
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$R/I$ or $R\!-\!I$ , quotient ring or difference ring of $R$ with respect to the ideal $I$
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$\operatorname{Z}(G)$ , center of the group $G$
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$R[G]$ , group ring of the group $G$ over the ring $R$
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$R[\alpha]$ , ring adjunction
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$K(\alpha)$ , field adjunction
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$S^{-1}R$ , localization of the ring $R$ at $S$
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$R_{\mathfrak{p}}$ , localization of the ring $R$ at the complement of the prime ideal $\mathfrak{p}$
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$(R,\,\mathfrak{m})$ , local ring $R$ with its maximal ideal $\mathfrak{m}$
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${}_{R}M$ , a left $R$ -module (http://planetmath.org/Module) $M$
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$M_{R}$ , a right $R$ -module (http://planetmath.org/Module) $M$
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$K/k$ , field extension where $K$ is an extension field of $k$
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$[K\!:\!k]$ , degree (http://planetmath.org/ExtensionField) of the field extension $K/k$
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$\overline{K}$ , algebraic closure of a field $K$
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$R\alpha_{1}+...+R\alpha_{n}$ or $\langle\alpha_{1},\,...,\,\alpha_{n}\rangle$ , left ideal of the ring $R$ generated by (http://planetmath.org/IdealGeneratedByASet) $\alpha_{1}$ , …, $\alpha_{n}$
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$A_{1}\cong A_{2}$ , isomorphism (http://planetmath.org/Isomorphism) between the systems (http://planetmath.org/AlgebraicSystem) $A_{1}$ and $A_{2}$

Title	special notations in algebra
Canonical name	SpecialNotationsInAlgebra
Date of creation	2013-03-22 15:11:50
Last modified on	2013-03-22 15:11:50
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	22
Author	Wkbj79 (1863)
Entry type	Topic
Classification	msc 08A99
Synonym	notations in algebra