## The New Encyclopaedia Britannica: Micropaedia. Ready Reference : A-Bayes, Volume 1 |

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Page 294

More technically,

commutative group M (written additively) endowed with a mapping of R X M into

M satisfying axioms to be listed. This mapping associates to every pair (a, x)

formed ...

More technically,

**given**a ring R, a left 7?-module (or a left module over R) is acommutative group M (written additively) endowed with a mapping of R X M into

M satisfying axioms to be listed. This mapping associates to every pair (a, x)

formed ...

Page 298

Now if a base (eh e2, • □ □ , ek) for V is

called the dual basis, by defining e* to be that linear functional on V

certain rules (see 350). Then the correspondence e, *-» e* sets up an

isomorphism ...

Now if a base (eh e2, • □ □ , ek) for V is

**given**, then a basis for V* may be set up,called the dual basis, by defining e* to be that linear functional on V

**given**bycertain rules (see 350). Then the correspondence e, *-» e* sets up an

isomorphism ...

Page 492

A manifold W with such Clx

is called a symplectic manifold. As before, for plectic each x, <p ax:Tji W) —* T*(

W) is an isomorphism from the manifold tangent space to its dual, the cotangent ...

A manifold W with such Clx

**given**for each x, Qx varying differentially Sym- with x,is called a symplectic manifold. As before, for plectic each x, <p ax:Tji W) —* T*(

W) is an isomorphism from the manifold tangent space to its dual, the cotangent ...

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The New Encyclopaedia Britannica: Micropaedia. Ready Reference : A ..., Volume 1 University of Chicago No preview available - 1991 |

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