In this note the notion of interval-valued fuzzy B-algebras (briefly,i-v fuzzy B-algebras), the level and strong level B-subalgebra is introduced.Then we state and prove some theorems which determine the relationshipbetween these notions and B-subalgebras. The images and inverse images ofi-v fuzzy B-subalgebras are defined, and how the homomorphic images andinverse images of i-v fuzzy B-subalge...

In this paper, we apply the concepts of fuzzy subsets to coalgebras and define fuzzy subcoalgebras and fuzzy left (right) coideals. Considering the applications of fuzzy subcoalgebras and fuzzy left (right) coideals, we discuss their properties under homomorphisms of coalgebras and the relationship among them. A fuzzy subcoalgebra and its duality as well as a fuzzy subalgebra and its duality is...

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...

The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

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...