Two exercises concerning the degree of the product of algebraic numbers | Zendy

Artūras Dubickas | Zendy

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Two exercises concerning the degree of the product of algebraic numbers

Author(s) -

Artūras Dubickas

Publication year - 2005

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim0591067d

Subject(s) - degree (music) , algebraic number , simple (philosophy) , mathematics , product (mathematics) , field (mathematics) , state (computer science) , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , physics , algorithm , geometry , philosophy , epistemology , acoustics

. Let k be a eld, and let and be two algebraic numbers over k of degree d and `, respectively. We nd necessary and su cient conditions under which deg( ) = d` and deg( + ) = d`. Since these conditions are quite di cult to check, we also state a simple su cient condition for such equalities to occur.

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