Extended Ockham Algebras And Demi-pseudocomplemented Double MS-algebras

A demi-pseudocomplementeted double MS-algebras is an algebra (L;∧,∨,°,+,*,0,1) of type (2,2,1,1,1,0,0) in which (L;°,+) is a double MS-algebra,(L;*) is a demi-pseudocomplemented algebra and the unary operations are linked by the identities x°*=x*°and x+*=x*+. In this thesis, we described principal congruence of the demi-pseudocomplemented double MS-algebras. The main results are given as follows:(A)[Theorem3.2.1] If (L;°,+,*) is a demi-pseudocomplementeted double MS-algebra, then Φ and G are congruences with Φ≤G, where Φ and G are given as follows:(x, y)∈Φ (?) x°=y°and x+=y+;(x,y)∈G (?) x*=y*.(B)[Theorem3.2.3] Let (L·°,+,*) be a demi-pseudocomplementeted double MS-algebra. If a,b E L are such that α≤b, then θ{a, b)=θDMS(a, b)∨θlat(b*, a*)∧lat(a°*, b°*)∨θlat(a+*, b+*) where θDMS(a,b) denotes the principal DMS-congruence associated with a and b,θlat(b*, a*) denotes principal lattice congruence associated with b*and a*.An extended Ockham algebra is an Ockham algebra (L;f) on which en-dowed with an endomorphism k satisfying the condition fk=kf. An extended Ockham algebra (L;f, k) is said to be of extended de Morgan skeleton, if the set S(L)={f2k2(x)|x∈L} is an extended de Morgan algebra. In this thesis, we characterized some structures of the isotone mappings on extended Ockham algebras. The main results we obtained in this thesis are given as follows:(C)[Theorem4.1.2] If L and M are extended Ockham algebras with extended de Morgan skeleton, then H(S(L),S(M))-S(H(L,M)).(D)[Theorem4.2.1] If (L;f, k) and (M;f, k) are extended MS-algebras then Fix H(L,M)=Max{α∈H(L,M)I((?)x∈L)α(f(x))=f(α(x))及α(k(x))=k(α(x))} where H(L,M)is the set of isotone mappings from L to M,Fix H(L,M)is a set of fixed points of (H(L,M);f,k).