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单词 Tame Algebra
释义

Tame Algebra

Let denote an -algebra, so that is a Vector Space over and




where is vector multiplication which is assumed to be Bilinear. Now define


where . is said to be tame if is a finite union of Subspaces of . A 2-D 0-Associativealgebra is tame, but a 4-D 4-Associative algebra and a 3-D 1-Associative algebra need not be tame. It isconjectured that a 3-D 2-Associative algebra is tame, and proven that a 3-D 3-Associative algebra is tameif it possesses a multiplicative Identity Element.


References

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


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