SQUARE-FREE DISCRIMINANTS OF FROBENIUS RINGS
نویسندگان
چکیده
منابع مشابه
Square-free discriminants of Frobenius rings
Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of Ep, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field Q(πp) generated by the Frobenius element πp. When the curve has complex multiplication (CM), this is always a fixed field as the prime varies. However, when the curve has no CM, very little is known, not...
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Finite-dimensional square-freeK-algebras have been completely characterized by Anderson and D’Ambrosia as certain semigroup algebras A ∼= KξS over a square-free semigroup S twisted by some ξ ∈ Z (S,K), a two-dimensional cocycle of S with coefficients in the group of units K∗ of K. D’Ambrosia extended the definition of square-free to artinian rings with unity and showed every square-free ring ha...
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Let R be a local ring of prime characteristic. We study the ring of Frobenius operators F(E), where E is the injective hull of the residue field of R. In particular, we examine the finite generation of F(E) over its degree zero component F0(E), and show that F(E) need not be finitely generated when R is a determinantal ring; nonetheless, we obtain concrete descriptions of F(E) in good generalit...
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Let |Λ| 6= Y be arbitrary. Recent developments in elementary representation theory [35] have raised the question of whether every finitely hyper-surjective, canonically contra-Jordan, sub-continuous hull is super-naturally φ-finite. We show that Θ is not greater than x̃. This reduces the results of [35] to an easy exercise. In [35], the authors address the degeneracy of quasi-Fréchet, holomorphi...
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The notion of FTF ring (see Definition 1.1 or Proposition 1.2) captures homological and finiteness properties shared by several classes of rings. Thus coherent rings with left flat-dominant dimension ≥ 1 [3, Corolario 2.2.11] or rings having quasi-Frobenius two-sided maximal quotient ring [7, Proposition 3.6; 3, Teorema 2.3.10] are examples of FTF rings. Moreover, FTF ring and QF-3 ring are rel...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2010
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042110003599