In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

These notes are based on Saltman’s seminal work on the Brauer group Br(K) of the function field K of a p-adic curve XQp . In [S1] and [S2], Saltman showed the index of an element in the prime-to-p part of Br(K) divides the square of its period, and that all division algebras of prime degree q 6= p are cyclic. He also gave a geometric criterion for a class of prime period q 6= p to have index q....

This paper gives new upper bounds on the stick numbers of knots [Formula: see text], and as well equilateral number text]. These imply that text] have superbridge index completing project showing no prime through 10 crossings can larger than 5. The current best for are given in Appendix A.

It is known that with a very small number of exceptions, for a term of a Lehmer sequence {Un( √ R,Q)} to be prime its index must be prime. For example, F4 = U4(1,−1) = 3 is prime. Also, Un(1, 2) is prime for n = 6, 8, 9, 10, 15, 25, 25, 65, while Vn(1, 2) is prime for n = 9, 12, and 20. This criterion extends to the companion Lehmer sequences {Vn( √ R,Q)}, with the exception that primality may ...

In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if $N$ is a weakly prime subtractive ternary subsemimodule of a ternary $R$-semimodule $M$, then either $N$ is a prime ternary subsemimodule or $(N : M)(N : M)N = 0$. If $N$ is a $Q$-...

let $g$ be a finite group and let $gk(g)$ be the prime graph of $g$. we assume that $ngeqslant 5 $ is an odd number. in this paper, we show that the simple groups $b_n(3)$ and $c_n(3)$ are 2-recognizable by their prime graphs. as consequences of the result, the characterizability of the groups $b_n(3)$ and $c_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are obtai...