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>>>"Hulpke" == Alexander Hulpke <hulpke@math.colostate.edu> writes:

Hulpke> However (as also noted) now GAP 4.2 will stop with an

Hulpke> error message (``No method found'') that indicates that

Hulpke> the capability to test invertibility of a matrix in this

Hulpke> ring has not been implemented.

Except that GAP does seem to be able to decide invertibility:

gap> R := Integers mod 9; (Integers mod 9) gap> S := FullMatrixAlgebra(R,2); ( (Integers mod 9)^[ 2, 2 ] ) gap> one := Identity(R); zero := Zero(R); ZmodnZObj( 1, 9 ) ZmodnZObj( 0, 9 ) gap> x := [[one,one],[zero,one]]; [ [ ZmodnZObj( 1, 9 ), ZmodnZObj( 1, 9 ) ], [ ZmodnZObj( 0, 9 ), ZmodnZObj( 1, 9 ) ] ] gap> IsUnit(S,x); true

And one can even generate SL(2,Z/9Z):

gap> y := [[one,zero],[one,one]]; [ [ ZmodnZObj( 1, 9 ), ZmodnZObj( 0, 9 ) ], [ ZmodnZObj( 1, 9 ), ZmodnZObj( 1, 9 ) ] ] gap> Order(Group(x,y)); 648 gap> 3*4*2*27; 648

It seems like the group just mentioned must be constructed

as a subgroup of Units(S). (??)

[Sorry if I'm creating too much noise on this list...]

All the best,

George

-- __O | George McNinch <mcninch.1@nd.edu> _-\<,_ | www.nd.edu/~gmcninch (_)/ (_) | Dept. Math, Univ. Notre Dame

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