“Associative Algebra”的概念、定义、习题解题方法及翻译-数学辞典

单词

Associative Algebra

释义

Associative Algebra

In simple terms, let , , and be members of an Algebra. Then the Algebra is said to be associativeif

(1)

where

denotes Multiplication. More formally, let

denote an

-algebra, so that

is aVector Space over

and

(2)

(3)

Then

is said to be

-associative if there exists an

-D Subspace

such that

(4)

for all

and

. Here, Vector Multiplication

is assumed to be Bilinear.An

-D

-associative Algebra is simply said to be ``associative.''

See also Associative

References

Finch, S. ``Zero Structures in Real Algebras.'' http://www.mathsoft.com/asolve/zerodiv/zerodiv.html.

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