We introduce the notion of Gröbner S-basis of an ideal of the free associative algebra K〈X〉 over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Gröbner S-bases of the ideal corresponding to the universal enveloping algebra of the free nilpotent of class 2 Lie algebra and of the T-ideal generated by the polynomial identity [x, y, z] = 0, w...

In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of and algebra. After it is shown that the axioms are independent, given some properties algebraic structure. Then stated relationship between defining unary operation on Also, presented deductive system ideal It defined an generated subset algebra, constructed new adding element to its ideal.

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

When combining languages for symbolic constraints, one is typically faced with the problem of how to treat \mixed" constraints. The two main problems are (1) how to deene a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a \free...

We define type A, type B, type C as well as C∗-semi-finite C∗-algebras. It is shown that a von Neumann algebra is a type A, type B, type C or C∗-semi-finite C∗-algebra if and only if it is, respectively, a type I, type II, type III or semi-finite von Neumann algebra. Moreover, any type I C∗-algebra is of type A (actually, type A coincides with the discreteness as defined by Peligrad and Zsidó),...

We consider the relationship between ideals of a BCI-algebra and order ideals of its adjoint semigroup. We show that (1) if I is an ideal, then I =M−1(M(I)), (2) M(M−1(J)) is the order ideal generated by J∩R(X), (3) if X is a BCK-algebra, then J =M(M−1(J)) for any order ideal J of X, thus, for each BCK-algebra X there is a one-to-one correspondence between the set (X) of all ideals of X and the...