Showing papers on "Idempotence published in 1986"

Unification under associativity and idempotence is of type nullary

Abstract: It is shown, that there exist a unification problem〈s=t〉 AI , for which the set of solutions under associativity and idempotence is not empty But\(\mu U\sum _{Al} \left( {s,t} \right)\), the complete and minimal subset of this set of solutions does not exist, ieA+I is of type nullary This is the first known standard first order theory with this unpleasant feature

Primitive noncommutative Jordan algebras with nonzero socle

Abstract: Let A be a nondegenerate noncommutative Jordan algebra over a field K of characteristic * 2. Defining the socle S(A) of A to be the socle of the plus algebra A', we prove that S(A) is an ideal of A; then we prove that if A has nonzero socle, A is prime if and only if it is primitive, extending a result of Osborn and Racine [6] for the associative case. We also describe the prime noncommutative Jordan algebras with nonzero socle and in particular the simple noncommutative Jordan algebras containing a completely primitive idempotent. In fact we prove that a nondegenerate prime noncommutative Jordan algebra with nonzero socle is either (i) a noncommutative Jordan division algebra, (ii) a simple flexible quadratic algebra over an extension of the base field, (iii) a nondegenerate prime (commutative) Jordan algebra with nonzero socle, or (iv) a K-subalgebra of Lw( V)(X) containing Fw(V) or of H(Lv(V),*)(x) containing H(Fv(V), *) where in the first case (V, W) is a pair of dual vector spaces over an associative division K-algebra D and X # 1/2 is a central element of D, and where in the second case V is self-dual with respect to an hermitian inner product (I), D has an involution a (x and X # 1/2 is a central element of D with X + A = 1.

On algebras with convolution structures for Laguerre polynomials

Abstract: In this paper we treat the convolution algebra connected with Laguerre polynomials which was constructed by Askey and Gasper [1]. For this algebra, we study the maximal ideal space, Wiener's general Tauberian theorem, spectral synthesis and Helson sets. We also study Sidon sets and idempotent measures for the algebras with dual convolution structures.

On conservative minimal operations

Abstract: Publisher Summary This chapter discusses a classification of minimal operation on finite sets provided by Rosenberg. Such an operations is always of one of the following five types: (1) unary; (2) binary idempotent; (3) ternary majority; (4) semiprojection; and (5) x + y + z in a boolean group. No nontrivial operations of type (1) or (5) are conservative on at least three element sets. An operation f is minimal if the clone [ f ] generated by f is minimal, and f is of minimal arity among the nontrivial operations in [ f ]. An operation g on a set A is called conservative if every subset of A is closed under g .

Idempotent measures on commutative hypergroups

Abstract: The analysis in this paper will be carried out on a (locally compact) commutative hypergroup. We adhere to the following notation. Let X be a locally compact Hausdorff space...

On idempotent algebras with $$p_n (\mathfrak{A}) = 2n$$

Abstract: In this paper we fully characterize algebras with the number of essentiallyn-ary polynomials pn=2n for alln⩾ (Theorem 1, §3). Using this characterization we prove that the sequence (0, 0, 4) has Gratzer's minimal extension property, and the minimal extension is just the sequence 〈0, 0, 4, 6, 8,...〉.

Some examples of compressible group algebras and of noncompressible group algebras

Abstract: A ring R with centre Z ( R ) is called compressible if Z ( eRe ) = eZ ( R ) e for any idempotent e of R . In this paper we shall give some examples of compressible group algebras and of noncompressible group algebras. These examples show that it is very difficult to judge the compressibility of a group algebra.

Interpolation in idempotent algebras

Abstract: This chapter presents a necessary and sufficient condition for algebras with a semi-projection to have the interpolation property. An algebra = is said to have the interpolation property if every finitary operation on A is a local algebraic function of . It is known that every nontrivial idempotent algebra has a binary idempotent operation, a Mal’cev function, a ternary majority function, or at least a ternary nontrivial semi-projection among its term functions. An algebra is said to be idempotent if its fundamental operations and consequently its term functions are idempotent. The chapter presents an assumption in which an algebra = is at least three element idempotent algebra such that any two distinct elements of A generate , then either has the interpolation property or is affine with respect to an abelian elementary p -group or a torsion-free and divisible group.