On the basis of the concept of grades of a fuzzy point to belongingness (∈) or quasi-coincident (q) or belongingness and quasi-coincident (∈ ∧q) or belongingness or quasi-coincident (∈ ∨q) in an intuitionistic fuzzy set of a ring, the notion of a (α,β )intuitionistic fuzzy subring and ideal is introduced by applying the Lukasiewicz 3-valued implication operator. Using the notion of fuzzy cut se...

1 Abstract The propagation of electrical excitation in a ring of cells described by the Noble, Beeler-Reuter (BR), Luo-Rudy I (LR I), and third-order simpliied (TOS) mathematical models is studied using computer simulation. For each of the models it is shown that after transition from steady-state circulation to quasi-periodicity achieved by shortening the ring length (RL), the action potential...

We compare several quasi-Frobenius-type properties for corings that appeared recently in literature and provide several new characterizations for each of these properties. By applying the theory of Galois comodules with a firm coinvariant ring, we can characterize a locally quasi-Frobenius (quasi-co-Frobenius) coring as a locally projective generator in its category of comodules.

The concepts of a prime ideal of a distributively generated (d.g.) nearring R, a prime d.g. near-ring and an irreducible R-group are introduced1). The annihilating ideal of an irreducible R-group with an R-generator is a prime ideal. Consequently we define a prime ideal to be primitively prime if it is the annihilating ideal of such an R-group, and a d.g. near-ring to be a primitively prime nea...

Frobenius bimodules are connected with Frobenius algebras and extensions. For instance, a ring extension φ : R → S is a Frobenius extension if and only if RSS is a Frobenius bimodule [1]. Brzeziński and Gómez-Torrecillas studied in [4] certain properties of comatrix corings in relation to properties of bimodules. In particular they showed that the comatrix coring [6] induced by any Frobenius bi...

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...

We describe and explain the fluxionality of B(13)(+). The chemical bonding analysis shows that the inner triangle of B(13)(+) is bound to the peripheral ring by delocalized bonds only, allowing a quasi-free rotation of the inner ring.

This paper was motivated by a problem left by Herzog and Hibi, namely to classify all unmixed polymatroidal ideals. In the particular case of polymatroidal ideals corresponding to discrete polymatroids of Veronese type, i.e ideals of Veronese type, we give a complete description of the associated prime ideals and then, we show that such an ideal is unmixed if and only if it is CohenMacaulay. We...