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 introduce intuitionistic fuzzy generalized beta continuous mappings and intuitionistic fuzzy generalized beta irresolute mappings. We investigate some of their properties. Also we provide some characterization of intuitionistic fuzzy generalized beta continuous mappings and intuitionistic fuzzy generalized beta irresolute mappings. INTRODUCTION Atanassov [1] introduced the noti...

Generalizing a result of Furstenberg, we show that for every infinite discrete group $G$, the Bernoulli flow $2^G$ is disjoint from minimal $G$-flow. From this, deduce algebra generated by functions $\mathfrak{A}(G)$ proper subalgebra $\ell^\infty(G)$ and enveloping semigroup universal $M(G)$ quotient $\beta G$. When $G$ countable, also prove any metrizable, $G$-flow, there exists free, it exis...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.

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...