Ideals In Demi-pseudocomplemented MS-algebras

A demi-pseudocomplemented MS-algebra is an algebra(L;?,?,°,*,0,1)of type<2,2,1,1,0,0>in which(L;°)is an MS-algebra,(L;*)is a demi-pseudocomplemented algebra and the operations x(?)x° and x(?)x*are linked by the identity x°*= x*°.Let L be a demi-pseudocomplemented MS-algebra.An ideal I of L is said to be(O,*)-ideal,if for any x?L,x?I(?)x°*?I.In this thesis,we identify the(O,*)-ideals of a demi-pseudocomplemented MS-algebra L as the kernels of the Boolean congruences on L.In particular,we show that these ideals are precisely the kernels of the congruences(?)on L such that the quotient algebra(L/(?);*)is a Boolean algebra,and that they form a sublattice of the lattice of ideals of L that is isomorphic to the interval[G,t]of the congruence lattice Con L of L where G is the Glivenko congruence and l is the universal congruence.