Given an extension of finite fields $F\subseteq L$, we study the number of the equivalence classes of $F$-vector subspaces of $L$ modulo multiplication by elements of $L$, obtaining an exact formula and some bounds. We then apply the results obtained to the study of the set of $F$-star operations on $L$, which correspond to star operations on a pseudo-valuation domain $R$.
Spirito, D. (2019). Vector subspaces of finite fields and star operations on pseudo-valuation domains. FINITE FIELDS AND THEIR APPLICATIONS, 56, 17-30 [10.1016/j.ffa.2018.11.001].
Vector subspaces of finite fields and star operations on pseudo-valuation domains
Spirito, Dario
2019-01-01
Abstract
Given an extension of finite fields $F\subseteq L$, we study the number of the equivalence classes of $F$-vector subspaces of $L$ modulo multiplication by elements of $L$, obtaining an exact formula and some bounds. We then apply the results obtained to the study of the set of $F$-star operations on $L$, which correspond to star operations on a pseudo-valuation domain $R$.File in questo prodotto:
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