Abstract
In this paper, we study some properties of the Hurwitz series ring HR (resp. Hurwitz polynomial ring hR), such as the flatness or the faithful flatness of HR / (f) (resp. hR / (f)), the strongly Hopfian property and the radical property of HR (resp. hR). We give some sufficient and necessary conditions for HR / (f) (resp. hR / (f)) to be flat or faithful flat. We also prove that the strongly Hopfian property transfer between R and HR (resp. hR), and some radicals of HR can be determined in terms of those of R, in case R satisfies some additional conditions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahmadi M, Moussavi A and Nourozi V, On skew Hurwitz serieswise Armendariz rings, Asian–European J. Math. 7 (2014) 1450036 (19 pages)
Benhissi A, Ideal structure of Hurwitz series rings, Beitrage Algebra Geom. 48 (2007) 251–256
Benhissi A, Basic properties of Hurwitz series rings, Ricerche. Mat. 61 (2012) 255–273
Benhissi A, Chain condition on annihilators and strongly Hopfian property in Hurwitz series ring, Algebra Colloquium 21 (2014) 635–646
Cartan H and Eilenberg S, Homological Algebra (1956) (Princeton, NJ: Princeton Univ. Press)
Frohn D, Modules with \(n\)-\(acc\) and \(acc\) on certain types of annihilators, J. Algebra 256 (2002) 467–483
Hmaimou A, Kaidi A and Sanchez Campos E, Generalized fitting modules and rings, J. Algebra 308 (2007) 199–214
Keigher W F, On the ring of Hurwitz series, Comm. Algebra 25 (1997) 1845–1859
Liu Z, Hermite and \(PS\)-rings of Hurwitz series, Comm. Algebra 28 (2000) 299–305
Rotman J J, An introduction to homological algebra (1979) (New York: Academic Press)
Rowen L H, Ring Theory I (1988) (San Diego: Academic Press Inc.)
Wang F, The flat residual rings of polynomials, Acta Mathematical Sinica 45 (2002) 1171–1176
Acknowledgements
This research is supported by the National Natural Science Foundation of China (11471108), the Natural Science Foundation of Hunan Province (2016JJ2050), the Scientific Research Foundation of Hunan Provincial Education Department (12B101) and the Teaching Reform Foundation of Hunan Province (G21316).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicating Editor: B Sury
Rights and permissions
About this article
Cite this article
Ouyang, L., Zheng, K., Zhou, Q. et al. Special properties of Hurwitz series rings. Proc Math Sci 128, 45 (2018). https://doi.org/10.1007/s12044-018-0427-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12044-018-0427-y