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RANKS OF RELATIVE-UNIT-GROUPS RELATED TO redset(f).
- Source :
-
Journal of Algebra & Its Applications . Apr2012, Vol. 11 Issue 2, p1250034-1-1250034-9. 9p. - Publication Year :
- 2012
-
Abstract
- Given an irreducible polynomial f in k[X1,..., Xn] (where k is a field) such that k is algebraically closed in the quotient field of A ≔ k[X1,...,Xn]/f k[X1,...,Xn], we show that k(f) is algebraically closed in k(X1,...,Xn). Further, if n ≥ 2 and char k = 0, then we show that the number of k-translates of f that are reducible in k[X1,..., Xn] is bounded above by the rank of U(A)/U(k). Finally, we prove a similar bound for the number of reducible composites of the form Γ(f) with Γ ∈ k[T] monic irreducible. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 11
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 74637346
- Full Text :
- https://doi.org/10.1142/S0219498811005580