‎‎Let $R$ be a multiplicative hyperring‎. In this paper‎, ‎we introduce and study the concept of n-absorbing hyperideal which is a generalization‎ ‎of prime hyperideal‎. ‎A proper hyperideal $I$ of $R$ is called an $n$-absorbing hyperideal of ‎$‎R‎$‎ if whenever $alpha_1o...oalpha_{n+1} subseteq I$ for $alpha_1,...,alpha_{n+1} in R$‎, ‎then there are $n$ of the $alpha_i^,$s whose product ...

Let R be a commutative hyperring with identity. We introduceand study prime fuzzy hyperideals of R. We investigate the Zariski topologyon FHspec(R), the spectrum of prime fuzzy hyperideals of R.

The concepts of L-fuzzy ideal generated by a L-fuzzy subset, L-fuzzy prime and completely prime ideal where L is a complete lattice are considered and some results are proved

Let p be a prime k|p−1, t = (p−1)/k and γ(k, p) be the minimal value of s such that every number is a sum of s k-th powers (mod p). We prove Heilbronn’s conjecture that γ(k, p) k1/2 for t > 2. More generally we show that for any positive integer q, γ(k, p) ≤ C(q)k1/q for φ(t) ≥ q. A comparable lower bound is also given. We also establish exact values for γ(k, p) when φ(t) = 2. For instance, whe...

This article deals with the rapid-equilibrium kinetics of the forward and reverse reactions together for the ordered and random enzyme-catalyzed A+B=P+Q and emphasizes the importance of reporting the values of the full set of equilibrium constants. Equilibrium constants that are not in the rate equation can be calculated for random mechanisms using thermodynamic cycles. This treatment is based ...

We give an analysis of the non-constructivity of the following basic result: if X and Y are simplicial sets and Y has the Kan extension property, then Y X also has the Kan extension property. By means of Kripke countermodels we show that even simple consequences of this basic result, such as edge reversal and edge composition, are not constructively provable. We also show that our unprovability...