| The existence of the tensor product makes the category Sup of complete lattices and join-preserving maps being the symmetric and monoidal closed.Now,there are three ways to describe the tensor product of complete lattice.We can study the tensor product of special complete lattice and the application in Quantale.We consider the following cancellation problem for the tensor product（?）:L?M≌N?M?L≌N.（*）We find the cancellation law（*）of tensor product of the full subcategory SSup in Sup is equivalent to the cancellation law（**）of cartesian product of posets in Pos,which is for posets X,Y,Z,there is:X×Z≌Y×Z?X ≌Y.（**）In 2004,Banaschewski and Lowen considered above problem.In this paper,we continuous to consider this problem.The structure of this thesis is organized as follows:Chapter One:Preliminaries.In this chapter,we introduce the concepts and relevant conclusions of posets and tensor product of complete lattices.Chapter Two:The cancellation law of the cartesian product in Pos.We continue to investigate the cancellation law（**）in Pos,and we shall give a new class of posets satisfying the cancellation law（**）.And we shall give a new way to construct the posets such that the posets are not the connected poset which can be cancelled.Finally we consider the cancellation law（**）in SSup of superalgebraic complete lattices with join-preserving maps and provide an equivalent condition such that the cancellation law of the cartesian product of superalgebraic complete lattices always holds,and we prove the cancellation law（**）always holds when X,Y and Z are the finite superalgebraic complete lattices.Chapter Three:The cancellation law of tensor product in Sup.We study the cancellation law（*）of the tensor product about the special complete lattices.when L,N satisfies the special condition,there is M（≠2）such that the cancellation law（*）of tensor product holds. |
