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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$H\u25c1G$, $H$ 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 $RI$, quotient ring^{} or difference ring of $R$ with respect to the ideal $I$

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$\mathrm{Z}(G)$, 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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${R}_{\U0001d52d}$, localization of the ring $R$ at the complement of the prime ideal^{} $\U0001d52d$

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$(R,\U0001d52a)$, local ring^{} $R$ with its maximal ideal^{} $\U0001d52a$

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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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$R{\alpha}_{1}+\mathrm{\dots}+R{\alpha}_{n}$ or $\u27e8{\alpha}_{1},\mathrm{\dots},{\alpha}_{n}\u27e9$, 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  20130322 15:11:50 
Last modified on  20130322 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 