Suppose that f (resp. g) is a modular form of integral (resp. half-integral) weight with coefficients in the ring of integers OK of a number field K. For any ideal m ⊂ OK , we bound the first prime p for which f | Tp (resp. g | Tp2) is zero (mod m). Applications include the solution to a question of Ono [AO] concerning partitions.

We give an example of a vector bundle E on a relative curve C → SpecZ such that the restriction to the generic fiber in characteristic zero is semistable but such that the restriction to positive characteristic p is not strongly semistable for infinitely many prime numbers p. Mathematical Subject Classification (2000): 11A41; 13A35; 14H60

Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. Then the global tame degree t(H) equals zero if and only if H is factorial (equivalently, |G| = 1). If |G| > 1, then D(G) ≤ t(H) ≤ 1 + D(G) (

Let p be an odd prime and m be a positive integer. In this paper, we prove that the one-error linear complexity over Fp of Sidelnikov sequences of length p − 1 is ( p+1 2 ) − 1, which is much less than its (zero-error) linear complexity.

We construct strongly walk-regular graphs as coset of the duals codes with three non-zero homogeneous weights over $${\mathbb {Z}}_{p^m},$$ for p a prime, and more generally chain rings depth m, residue field size q, prime power. In case $$p=m=2,$$ strong necessary conditions ( diophantine equations) on weight distribution are derived, leading to partial classification in modest length. Infinit...

This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.

Objectives/Background: The ternary seminear ring is the generalization of and it need not be a semiring. Characterization quotient rings some structures have been analysed also studied ideals in rings. Further quasi defined discussed about their properties. Methods: Properties semiring employed to carry out this research work obtain all characterizations corresponding that Findings: We call an ...

A hybrid cloud is a cloud computing environment in which an organization provides and manages some internal resources and has others provided externally. However, this new environment could bring irretrievable losses to the clients due to a lack of integrity verification mechanism for distributed data outsourcing. To support scalable service and data migration, in this paper we address the cons...

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...