Composite Hurwitz Rings as PF-Rings and PP-Rings

Dong Kyu Kim and Jung Wook Lim
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Dong Kyu Kim: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 41566, Korea
Jung Wook Lim: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 41566, Korea

Mathematics, 2020, vol. 8, issue 1, 1-15

Abstract: Let R ⊆ T be an extension of commutative rings with identity and H ( R , T ) (respectively, h ( R , T ) ) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring). In this article, we study equivalent conditions for the rings H ( R , T ) and h ( R , T ) to be PF-rings and PP-rings. We also give some examples of PP-rings and PF-rings via the rings H ( R , T ) and h ( R , T ) .

Keywords: composite Hurwitz series ring; composite Hurwitz polynomial ring; McCoy condition; PF-ring; PP-ring; annihilator; idempotent element; torsion-free ?-module (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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