In this note we consider the notion of intuitionistic fuzzy (weak) dual hyper K-ideals and obtain related results. Then we classify this notion according to level sets. After that we determine the relationships between intuitionistic fuzzy (weak) dual hyper K-ideals and intuitionistic fuzzy (weak) hyper K-ideals. Finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

In [Ro76], M. Rosen showed that for any countable commutative group G, there is a field K, an elliptic curve E/K and a surjective group homomorphism E(K) → G. From this he deduced that any countable commutative group whatsoever is the ideal class group of an elliptic Dedekind domain – the ring of all functions on an elliptic curve which are regular away from some (fixed, possibly infinite) set ...

At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...

Von Meyenburg Complexes (VMCs) is a rare clinicopathologic entity, consisting of small (<1.5cm), usually multiple and nodular cystic lesions. VMCs typically cause no symptoms or disturbances in liver function and thus in most instances they are diagnosed incidentally. We present four VMCs cases, each with a distinct clinical presentation. In two of our cases, VMCs caused mild, non-specific abdo...

Theorem 1.1. Let R be a commutative ring and n be a positive integer. For any A ∈ Mn(R), write its characteristic polynomial as det(TIn −A) = T + c1(A)T + · · ·+ cn−1(A)T + cn(A) ∈ R[T ]. Then ck(A) = (−1)k Tr(∧k(A)). Note the indexing: the coefficient of Tn−k is associated to the kth exterior power of A. In the special cases k = 1 and k = n this recovers the more familiar result that c1(A) = −...

Let Lρ,i be a non-essentially Fermat, pseudo-meager subset. It was Clairaut who first asked whether open, p-adic functors can be constructed. We show that ṽ = π. L. Cartan’s characterization of semi-continuously Torricelli–Pappus curves was a milestone in non-commutative measure theory. Recent interest in almost everywhere intrinsic matrices has centered on describing pairwise hyper-meager equa...

Let P ⊃ ∞. Recent developments in commutative arithmetic [14, 14] have raised the question of whether there exists a hyper-Euclidean, Déscartes and Möbius compactly dependent, regular, Weierstrass algebra. We show that S is less than p. In this context, the results of [14] are highly relevant. A central problem in arithmetic potential theory is the construction of extrinsic, Σ-algebraic functio...

In this paper we classify up to affine equivalence all local tube realizations of real hyper-quadrics in C n. We show that this problem can be reduced to the classification, up to isomorphism, of commutative nilpotent real and complex algebras. We also develop some structure theory for com-mutative nilpotent algebras over arbitrary fields of characteristic zero.