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special notations in algebra
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(Topic)
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- $[G\!:\!H]$ , index 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 $R$
- $R[\alpha]$ , simple ring adjunction
- $K(\alpha)$ , simple 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 $M$
- $M_{R}$ , a right $R$ -module $M$
- $K/k$ , field extension where $K$ is an extension field of $k$
- $[K\!:\!k]$ , degree 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 $\alpha_1$ , ..., $\alpha_n$
- $A_1 \cong A_2$ , isomorphism between the systems $A_1$ and $A_2$
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"special notations in algebra" is owned by Wkbj79. [ full author list (7) | owner history (1) ]
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| Other names: |
notations in algebra |
This object's parent.
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Cross-references: left ideal, field, algebraic closure, extension field, field extension, right, maximal ideal, local ring, prime ideal, complement, localization, field adjunction, ring adjunction, ring, group ring, center, ideal, quotient ring, quotient group, normal subgroup, group, subgroup
There are 2 references to this entry.
This is version 19 of special notations in algebra, born on 2005-04-17, modified 2008-12-21.
Object id is 6955, canonical name is SpecialNotationsInAlgebra.
Accessed 3243 times total.
Classification:
| AMS MSC: | 08A99 (General algebraic systems :: Algebraic structures :: Miscellaneous) |
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Pending Errata and Addenda
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