ON THE CARMICHAEL RINGS, CARMICHAEL IDEALS AND CARMICHAEL POLYNOMIALS

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 82
  • Download : 0
Motivated by Carmichael numbers, we say that a finite ring R is a Carmichael ring if a(vertical bar R vertical bar) = a for any a is an element of R. We then call an ideal I of a ring R a Carmichael ideal if R/I is a Carmichael ring, and a Carmichael element of R means it generates a Carmichael ideal. In this paper, we determine the structure of Carmichael rings and prove a generalization of Korselt's criterion for Carmichael ideals in Dedekind domains. We extend several results from the number field case to the function field case. In particular, we study Carmichael elements of polynomial rings over finite fields (called Carmichael polynomials) by generalizing some classical results. For example, we show that there are infinitely many Carmichael polynomials but they have zero density.
Publisher
ARS POLONA-RUCH
Issue Date
2023-01
Language
English
Article Type
Article
Citation

COLLOQUIUM MATHEMATICUM, v.171, no.1, pp.1 - 17

ISSN
0010-1354
DOI
10.4064/cm8601-1-2022
URI
http://hdl.handle.net/10203/305351
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0