In this paper, the notions of L-fuzzy subalgebra degree and L-subalgebras on an effect algebra are introduced some characterizations given. We use four kinds cut sets L-subsets to characterize degree. induce convexity by degree, we prove that a morphism between two algebras is preserving mapping monomorphism convex-to-convex mapping. Finally, it proved set all can form L-convexity, its L-convex...

Z. Takáč in [16] introduced the aggregation operators on any subalgebra of M (set of all fuzzy membership degrees of the type-2 fuzzy sets, that is, the functions from [0,1] to [0,1]). Furthermore, he applied the Zadeh’s extension principle (see [24]) to obtain in [16, 17] a set of aggregation operators on L* (the strongly normal and convex functions of M). In this paper, we introduce the aggre...

In this note, we characterize Chebyshev subalgebras of unital JB-algebras. We exhibit that if B is Chebyshev subalgebra of a unital JB-algebra A, then either B is a trivial subalgebra of A or A= H R .l, where H is a Hilbert space

For an ideal or K-subalgebra E of K[X1, . . . , Xn], consider subfields k ⊂ K, where E is generated – as ideal or K-subalgebra – by polynomials in k[X1, . . . , Xn]. It is a standard result for ideals that there is a smallest such k. We give an algorithm to find it. We also prove that there is a smallest such k for K-subalgebras. The ideal results use reduced Gröbner bases. For the subalgebra r...

We show that the braided tensor product algebra A1⊗A2 of two module algebras A1,A2 of a quasitriangular Hopf algebraH is equal to the ordinary tensor product algebra of A1 with a subalgebra of A1⊗A2 isomorphic to A2, provided there exists a realization of H within A1. In other words, under this assumption we construct a transformation of generators which ‘decouples’ A1,A2 (i.e. makes them commu...

In this paper we continue our study of the Frattini p-subalgebra of a Lie />-algebra L. We show first that if L is solvable then its Frattini p-subalgebra is an ideal of L. We then consider Lie p-algebras L in which X. is nilpotent and find necessary and sufficient conditions for the Frattini p-subalgebra to be trivial. From this we deduce, in particular, that in such an algebra every ideal als...

Moreover the term predicate fuzzy logic L∀ will denote the predicate calculus obtained from the propositional core fuzzy logic L by adding the “classical” quantifiers (∀ and ∃) together with the same axioms and rule of generalization used by Hàjek in his book [7] when defining BL∀. On the other hand, given a left-continuous t-norm ∗, if L∗ denotes the (propositional) fuzzy logic which is standa...