منابع مشابه
Carlitz Extensions
The ring Z has many analogies with the ring Fp[T ], where Fp is a field of prime size p. For example, for nonzero m ∈ Z and nonzero M ∈ Fp[T ], the residue rings Z/(m) and Fp[T ]/M are both finite. The unit groups Z × = {±1} and Fp[T ]× = Fp are both finite. Every nonzero integer can be made positive after multiplication by a suitable unit, and every nonzero polynomial in Fp[T ] can be made mon...
متن کاملThe Carlitz Algebras
The Carlitz Fq-algebra C = Cν , ν ∈ N, is generated by an algebraically closed field K (which contains a non-discrete locally compact field of positive characteristic p > 0, i.e. K ≃ Fq[[x, x−1]], q = pν), by the (power of the) Frobenius map X = Xν : f 7→ f q, and by the Carlitz derivative Y = Yν. It is proved that the Krull and global dimensions of C are 2, a classification of simple C-modules...
متن کاملGeneralizations of Carlitz Compositions
We consider a class of generating functions that appear in the context of Carlitz compositions. In order to combinatorially interpret them, we introduce a combinatorial structures that we name generalized compositions and p-Carlitz compositions of integers. We explain their connection to Carlitz compositions, the relation to other combinatorial structures, and we describe their basic properties...
متن کاملOn Carlitz Compositions
This paper deals with Carlitz compositions of natural numbers (adjacent parts have to be different). The following parameters are analysed: number of parts, number of equal adjacent parts in ordinary compositions, largest part, Carlitz compositions with zeros allowed (correcting an erroneous formula from Carlitz). It is also briefly demonstrated that so-called 1-compositions of a natural number...
متن کاملForeword Leonard
Much has changed in computer security since 1973, when the Bell-LaPadula model was first published. Development has moved away from kernel-based secure systems toward application-level security capabilities, providing secure transactions on top of commercial, nonsecure operating systems. The potential for widespread use of encryption for privacy, authentication, and other services, as embodied ...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2000
ISSN: 1071-5797
DOI: 10.1006/ffta.2000.0276