Bibliographic Details
| Title: |
On ideal class groups of totally degenerate number rings. |
| Authors: |
Hambardzumyan, Ruben1 (AUTHOR) ruben.hambardzumyan2@edu.ysu.am, Papikian, Mihran1,2 (AUTHOR) papikian@psu.edu |
| Source: |
Journal of Number Theory. May2026, Vol. 282, p118-143. 26p. |
| Subjects: |
Class groups (Mathematics), Polynomials, Asymptotic expansions, Ordered algebraic structures, Integers |
| Abstract: |
Let χ (x) ∈ Z [ x ] be a monic polynomial whose roots are distinct integers. We study the ideal class monoid and the ideal class group of the ring Z [ x ] / (χ (x)). We obtain formulas for the orders of these objects, and study their asymptotic behavior as the discriminant of χ (x) tends to infinity, in analogy with the Brauer-Siegel theorem. Finally, we describe the structure of the ideal class group when the degree of χ (x) is 2 or 3. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
