JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 3, Pages 591 - 602
(December 2005)
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ON A LOCALIZATION OF THE LAURENT POLYNOMIAL RING
Sami Barhoumi (Tunisia) and Ihsen Yengui (Tunisia)
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Abstract: We give a description of the prime spectrum of the localization of the Laurent polynomial ring R[X, X?1] at doubly monic polynomials using its interactions with the rings and respectively the localizations of the rings R[X], R[X?1],and R[X?1 + X] at monic polynomials. We also give the analogue of Horrock?s theorem for Laurent polynomial rings. In fact, we provide a process to systematically translate the results related to Serre?s conjecture and modules over R[X1, ?, Xn] to modules over the multivariate Laurent polynomial ring |
Keywords and phrases: localization of polynomial ring, Krull dimension, valuative dimension, projective modules. |
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