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- Title
About the Entropy of a Natural Number and a Type of the Entropy of an Ideal.
- Authors
Minculete, Nicuşor; Savin, Diana
- Abstract
In this article, we find some properties of certain types of entropies of a natural number. We are studying a way of measuring the "disorder" of the divisors of a natural number. We compare two of the entropies H and H ¯ defined for a natural number. An useful property of the Shannon entropy is the additivity, H S (pq) = H S (p) + H S (q) , where pq denotes tensor product, so we focus on its study in the case of numbers and ideals. We mention that only one of the two entropy functions discussed in this paper satisfies additivity, whereas the other does not. In addition, regarding the entropy H of a natural number, we generalize this notion for ideals, and we find some of its properties.
- Subjects
NATURAL numbers; ENTROPY; UNCERTAINTY (Information theory); ALGEBRAIC field theory; ALGEBRAIC number theory; TENSOR products; TOPOLOGICAL entropy
- Publication
Entropy, 2023, Vol 25, Issue 4, p554
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e25040554