User:Inthar/Style guide: Difference between revisions
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== Algebraic structures == | == Algebraic structures == | ||
* <math>\mathrm{JI}\langle p_1, ..., p_r \rangle</math> is the ''p''<sub>1</sub>.[...].''p''<sub>''r''</sub> subgroup, the subgroup of <math>(\mathbb{Q}_{>0}, \cdot)</math> generated by rationals <math>p_1, ..., p_r.</math> | * <math>\mathrm{JI}\langle p_1, ..., p_r \rangle</math> is the ''p''<sub>1</sub>.[...].''p''<sub>''r''</sub> subgroup, the subgroup of <math>(\mathbb{Q}_{>0}, \cdot)</math> generated by rationals <math>p_1, ..., p_r.</math> For not-necessarily-JI generators, <math>\mathrm{M}\langle p_1, ..., p_r \rangle</math> is used. | ||
* If ''R'' is a commutative ring with 1, <math>R^r\langle a_1, ..., a_r\rangle</math> is the rank-''r'' free ''R''-module generated by basis elements <math>a_1, ..., a_r.</math> Ordered tuples in such modules are assumed to be in the given basis. Example: <math>\mathbf{m} + 3\mathbf{s} = (0,1,3) \in \mathbb{Z}^3\langle \mathbf{L}, \mathbf{m}, \mathbf{s}\rangle</math> | * If ''R'' is a commutative ring with 1, <math>R^r\langle a_1, ..., a_r\rangle</math> is the rank-''r'' free ''R''-module generated by basis elements <math>a_1, ..., a_r.</math> Ordered tuples in such modules are assumed to be in the given basis. Example: <math>\mathbf{m} + 3\mathbf{s} = (0,1,3) \in \mathbb{Z}^3\langle \mathbf{L}, \mathbf{m}, \mathbf{s}\rangle</math> | ||