Let $G$ be a finitely generated abelian group and $M$ be a $G$-graded $A$-module. In general, $G$-associated prime ideals to $M$ may not exist. In this paper, we introduce the concept of $G$-attached prime ideals to $M$ as a generalization of $G$-associated prime ideals which gives a connection between certain $G$-prime ideals and $G$-graded modules over a (not necessarily $G$-graded Noetherian...

Is it possible to improve the convergence properties of the series for the computation of the Cn involved in the distribution of the generalized Fermat prime numbers? If the answer to this question is yes, then the search for a large prime number P will be C · log(P ) times faster than today, where C ≈ 0.01.

By making use of only simple facts about congruence, we first show that every even Markoff number is congruent to 2 modulo 32, and then establish the uniqueness for those Markoff numbers c where one of 3c − 2 and 3c + 2 is a prime power, 4 times a prime power, or 8 times a prime power.

Let K′ be a knot that admits no cosmetic crossing changes and let C be a prime, non-cable knot. Then any knot that is a satellite of C with winding number zero and pattern K′ admits no cosmetic crossing changes. As a consequence we prove the nugatory crossing conjecture for Whitehead doubles of prime, non-cable knots.

In [2], we gave algorithms to calculate c(G), q(G) and p(G) for a finite group G. In this paper, we show that for a finite p-group G, where p is a prime, q(G) = p(G). Moreover, for odd prime p, c(G) = q(G) = p(G). 2000 Mathematics Subject Classification: primary 20D15; secondary 20B05, 20C15

Abstract Let $\textsf{T}$ be a triangulated category with shift functor $\Sigma \colon \textsf{T} \to \textsf{T}$ . Suppose $(\textsf{A},\textsf{B})$ is co-t-structure coheart $\textsf{S} = \Sigma \textsf{A} \cap \textsf{B}$ and extended $\textsf{C} \Sigma^2 \textsf{B} \textsf{S}* \textsf{S}$ , which an extriangulated category. We show that there bijection between co-t-structures $(\textsf{A}^{...

Various topics on affine rings are considered, such as the relationship between Gelfand-Kirillov dimension and Krull dimension, and when a "locally affine" algebra is affine. The dimension result is applied to study prime ideals in fixed rings of finite groups, and in identity components of group-graded rings. 0. Introduction. We study affine rings (i.e., rings finitely generated as algebras ov...

In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.

in this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. we study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. for strongly z-ideals, we analyze prime ideals using the concept of zero sets. moreover, it is proven that the intersection of all zero sets of a prime ideal of c(l),...