We prove that the curve Y0(p) has no F2(T )-rational points where p ⊳ F2[T ] is a prime ideal of degree at least 3 and Y0(p) is the affine Drinfeld modular curve parameterizing Drinfeld modules of rank two over F2[T ] of general characteristic with Hecke-type level p-structure. As a consequence we derive a conjecture of Schweizer describing completely the torsion of Drinfeld modules of rank two...

Let R be a commutative ring with nonzero identity, Z(R) be its set of zero-divisors, Nil(R) be its ideal of nilpotent elements, and U(R) be its group of units. We define a nonempty proper subset H of R to be a multiplicative-prime subset of R if the following two conditions hold: (i) ab ∈ H for every a ∈ H and b ∈ R; (ii) if ab ∈ H for a, b ∈ R, then either a ∈ H or b ∈ H . For example, H is mu...

The main result of this paper states that if R is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of R is a principal right ideal ring then R is right hereditary. In [10, Theorem 8] it is proved that if R is a right bounded prime ring of finite right Goldie dimension such that every proper homomorphic image is a...

In this paper we study certain families of right ideals in noncommutative rings, called right Oka families, generalizing previous work on commutative rings by T.Y. Lam and the author. As in the commutative case, we prove that the right Oka families in a ring R correspond bijectively to the classes of cyclic right R-modules that are closed under extensions. We define completely prime right ideal...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

This paper presents a criterion for testing the irreducibility of a polynomial over an algebraic extension field. Using this criterion and the characteristic set method, the authors give a criterion for testing whether certain difference ascending chains are strong irreducible, and as a consequence, whether the saturation ideals of these ascending chains are prime ideals.

IN HIS WORK on complex cobordism [ 181 Novikov introduced a spectral sequence converging to the stable homotopy of a space, depending only on the complex cobordism of the space as a module over the ring of primary complex cobordism operations. This spectral sequence can be localized at a prime p and one can work, as Novikov did, with the smaller theory, BP*( ), known as Brown-Peterson cohomolog...

Following an idea of Kronecker, we describe a method for factoring prime ideal extensions in number rings. The method needs factorization of polynomials in many variables over finite fields, but it works for any prime and any number field extension. Introduction Let F c K be number fields, let ¿fp c <?* be their corresponding number rings, i.e., the integral closures of Z in F and K, respective...