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Let F be an algebraically closed field of characteristic zero and L an RA loop. We prove that the loop algebra FL is in the variety generated by the split Cayley–Dickson algebra Z F over F. For RA2 loops of type M(Dih(A), ?1,g 0), we prove that the loop algebra is in the variety generated by the algebra 3 which is a noncommutative simple component of the loop algebra of a certain RA2 loop of order 16. The same does not hold for the RA2 loops of type M(G, ?1,g 0), where G is a non-Abelian group of exponent 4 having exactly 2 squares. 相似文献
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Jerzy Browkin. 《Mathematics of Computation》2004,73(246):1031-1037
We define some new kinds of pseudoprimes to several bases, which generalize strong pseudoprimes. We call them Sylow -pseudoprimes and elementary Abelian -pseudoprimes. It turns out that every which is a strong pseudoprime to bases 2, 3 and 5, is not a Sylow -pseudoprime to two of these bases for an appropriate prime
We also give examples of strong pseudoprimes to many bases which are not Sylow -pseudoprimes to two bases only, where or
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We derive explicit factorizations of generalized cyclotomic polynomials of order and generalized Dickson polynomials of the first kind of order over finite field . 相似文献
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The k-subset sum problem over finite fields is a classical NP-complete problem. Motivated by coding theory applications, a more complex problem is the higher m-th moment k-subset sum problem over finite fields. We show that there is a deterministic polynomial time algorithm for the m-th moment k-subset sum problem over finite fields for each fixed m when the evaluation set is the image set of a monomial or Dickson polynomial of any degree n. In the classical case , this recovers previous results of Nguyen-Wang (the case ) [22] and the results of Choe-Choe (the case ) [3]. 相似文献
36.
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive properties in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev polynomials and some formulas with a number-theoretic flavor. This paper is an abridged version of two articles by the author. 相似文献
38.
《Expositiones Mathematicae》2020,38(4):537-547
We provide proofs for the fact that certain orders have no infinite descending chains and no infinite antichains. 相似文献
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Giordano Gallina 《代数通讯》2018,46(7):2905-2911
We study the ideals in some Dickson nearrings of polynomials and formal power series. For some of their related quotients, we introduce variants and generalizations, and construct composition rings also. 相似文献
40.
By using the piecewise method, Lagrange interpolation formula and Lucas' theorem, we determine explicit expressions of the inverses of a class of reversed Dickson permutation polynomials and some classes of generalized cyclotomic mapping permutation polynomials over finite fields of characteristic three. 相似文献