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Composite Hurwitz Rings as PF-Rings and PP-Rings

Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 41566, Korea
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Mathematics 2020, 8(1), 100; https://doi.org/10.3390/math8010100
Received: 4 December 2019 / Revised: 2 January 2020 / Accepted: 3 January 2020 / Published: 7 January 2020
(This article belongs to the Special Issue Algebra and Discrete Mathematics)
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 ) . View Full-Text
Keywords: composite Hurwitz series ring; composite Hurwitz polynomial ring; McCoy condition; PF-ring; PP-ring; annihilator; idempotent element; torsion-free ℤ-module composite Hurwitz series ring; composite Hurwitz polynomial ring; McCoy condition; PF-ring; PP-ring; annihilator; idempotent element; torsion-free ℤ-module
MDPI and ACS Style

Kim, D.K.; Lim, J.W. Composite Hurwitz Rings as PF-Rings and PP-Rings. Mathematics 2020, 8, 100.

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