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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | )abbrev category NAALG NonAssociativeAlgebra
++ Author: J. Grabmeier, R. Wisbauer
++ Date Created: 01 March 1991
++ Date Last Updated: 11 June 1991
++ Reference:
++ R.D. Schafer: An Introduction to Nonassociative Algebras
++ Academic Press, New York, 1966
++ Description:
++ NonAssociativeAlgebra is the category of non associative algebras
++ (modules which are themselves non associative rngs).\br
++
++ Axioms\br
++ \tab{5}r*(a*b) = (r*a)*b = a*(r*b)
NonAssociativeAlgebra(R) : Category == SIG where
R : CommutativeRing
SIG ==> Join(NonAssociativeRng, Module(R)) with
plenaryPower : (%,PositiveInteger) -> %
++ plenaryPower(a,n) is recursively defined to be
++ \spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \spad{n>1}
++ and \spad{a} for \spad{n=1}.
add
plenaryPower(a,n) ==
( n = 1 ) => a
n1 : PositiveInteger := (n-1)::NonNegativeInteger::PositiveInteger
plenaryPower(a,n1) * plenaryPower(a,n1)
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