# special notations in algebra

• $[G\!:\!H]$,   index (http://planetmath.org/Coset) of a subgroup $H$ in the group $G$

• $H\triangleleft G$,   $H$ is a normal subgroup of $G$

• $G/H$,   quotient group of $G$ with respect to the normal subgroup $H$

• $R/I$ or $R\!-\!I$,   quotient ring or difference ring of $R$ with respect to the ideal $I$

• $\operatorname{Z}(G)$,   center of the group $G$

• $R[G]$,   group ring of the group $G$ over the ring $R$

• $R[\alpha]$,   ring adjunction

• $K(\alpha)$,   field adjunction

• $S^{-1}R$,   localization of the ring $R$ at $S$

• $R_{\mathfrak{p}}$,   localization of the ring $R$ at the complement of the prime ideal $\mathfrak{p}$

• $(R,\,\mathfrak{m})$,   local ring $R$ with its maximal ideal $\mathfrak{m}$

• ${}_{R}M$,   a left $R$-module (http://planetmath.org/Module) $M$

• $M_{R}$,   a right $R$-module (http://planetmath.org/Module) $M$

• $K/k$,   field extension where $K$ is an extension field of $k$

• $[K\!:\!k]$,   degree (http://planetmath.org/ExtensionField) of the field extension $K/k$

• $\overline{K}$,   algebraic closure of a field $K$

• $R\alpha_{1}+...+R\alpha_{n}$  or  $\langle\alpha_{1},\,...,\,\alpha_{n}\rangle$,   left ideal of the ring $R$ generated by (http://planetmath.org/IdealGeneratedByASet) $\alpha_{1}$, …, $\alpha_{n}$

• $A_{1}\cong A_{2}$,   isomorphism (http://planetmath.org/Isomorphism) between the systems (http://planetmath.org/AlgebraicSystem) $A_{1}$ and $A_{2}$

Title special notations in algebra SpecialNotationsInAlgebra 2013-03-22 15:11:50 2013-03-22 15:11:50 Wkbj79 (1863) Wkbj79 (1863) 22 Wkbj79 (1863) Topic msc 08A99 notations in algebra