Keywords: skew Hurwitz series ring; $\omega $-compatible ring; skew Hurwitz serieswise; quasi-Armendariz rings; zip ring; APP ring
@article{10_21136_MB_2023_0031_22,
author = {Sharma, Rajendra Kumar and Singh, Amit B.},
title = {On a theorem of {McCoy}},
journal = {Mathematica Bohemica},
pages = {27--38},
year = {2024},
volume = {149},
number = {1},
doi = {10.21136/MB.2023.0031-22},
mrnumber = {4715554},
zbl = {07830541},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0031-22/}
}
Sharma, Rajendra Kumar; Singh, Amit B. On a theorem of McCoy. Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 27-38. doi: 10.21136/MB.2023.0031-22
[1] Ahmadi, M., Moussavi, A., Nourozi, V.: On skew Hurwitz serieswise Armendariz rings. Asian-Eur. J. Math. 7 (2014), Article ID 1450036, 19 pages. | DOI | MR | JFM
[2] Annin, S.: Associated primes over Ore extensions rings. J. Algera Appl. 3 (2004), 193-205. | DOI | MR | JFM
[3] Armendariz, E. P.: A note on extensions of Baer and P.P.-rings. J. Aust. Math. Soc. 18 (1974), 470-473. | DOI | MR | JFM
[4] Beachy, J. A., Blair, W. D.: Rings whose faithful left ideals are cofaithful. Pac. J. Math. 58 (1975), 1-13. | DOI | MR | JFM
[5] Benhissi, A., Koja, F.: Basic properties of Hurwitz series rings. Ric. Mat. 61 (2012), 255-273. | DOI | MR | JFM
[6] Birkenmeier, G. F., Kim, J. Y., Park, J. K.: On quasi-Baer rings. Algebra and Its Applications Contemporary Mathematics 259. AMS, Providence (2000), 67-92. | DOI | MR | JFM
[7] Cedó, F.: Zip rings and Mal'cev domains. Commun. Algebra 19 (1991), 1983-1991. | DOI | MR | JFM
[8] Cortes, W.: Skew polynomial extensions over zip rings. Int. J. Math. Math. Sci. 2008 (2008), Article ID 496720, 9 pages. | DOI | MR | JFM
[9] Faith, C.: Rings with zero intersection property on annihilators: Zip rings. Publ. Mat., Barc. 33 (1989), 329-338. | DOI | MR | JFM
[10] Faith, C.: Annihilator ideals, associated primes and Kasch-McCoy commutative rings. Commun. Algebra 19 (1991), 1867-1892. | DOI | MR | JFM
[11] Fields, D. E.: Zero divisors and nilpotent elements in power series rings. Proc. Am. Math. Soc. 27 (1971), 427-433. | DOI | MR | JFM
[12] Fliess, M.: Sur divers produits de séries formelles. Bull. Soc. Math. Fr. 102 (1974), 181-191 French. | DOI | MR | JFM
[13] Gilmer, R., Grams, A., Parker, T.: Zero divisors in power series rings. J. Reine Angew. Math. 278/279 (1975), 145-164. | DOI | MR | JFM
[14] Hashemi, E., Moussavi, A.: Polynomial extensions of quasi-Baer rings. Acta. Math. Hung. 107 (2005), 207-224. | DOI | MR | JFM
[15] Hassanein, A. M.: Clean rings of skew Hurwitz series. Matematiche 62 (2007), 47-54. | MR | JFM
[16] Hirano, Y.: On annihilator ideals of a polynomial ring over a noncommutative ring. J. Pure Appl. Algebra 168 (2002), 45-52. | DOI | MR | JFM
[17] Hong, C. Y., Kim, N. K., Kwak, T. K., Lee, Y.: Extensions of zip rings. J. Pure Appl. Algebra 195 (2005), 231-242. | DOI | MR | JFM
[18] Hong, C. Y., Kim, N. K., Lee, Y.: Extensions of McCoy's theorem. Glasg. Math. J. 52 (2010), 155-159. | DOI | MR | JFM
[19] Jones, L. G., Weiner, L.: Advanced problems and solutions: Solutions 4419. Concerning a theorem of McCoy. Am. Math. Mon. 59 (1952), 336-337. | DOI | MR
[20] Keigher, W. F.: Adjunctions and comonads in differential algebra. Pac. J. Math. 59 (1975), 99-112. | DOI | MR | JFM
[21] Keigher, W. F.: On the ring of Hurwitz series. Commun. Algebra 25 (1997), 1845-1859. | DOI | MR | JFM
[22] Keigher, W. F., Pritchard, F. L.: Hurwitz series as formal functions. J. Pure Appl. Algebra 146 (2000), 291-304. | DOI | MR | JFM
[23] Krempa, J.: Some examples of reduced rings. Algebra Colloq. 3 (1996), 289-300. | MR | JFM
[24] Leroy, A., Matczuk, J.: Zip property of certain ring extensions. J. Pure Appl. Algebra 220 (2016), 335-345. | DOI | MR | JFM
[25] Liu, Z., Zhao, R.: A generalization of PP-rings and p.q.-Baer rings. Glasg. Math. J. 48 (2006), 217-229. | DOI | MR | JFM
[26] McCoy, N. H.: Remarks on divisors of zero. Am. Math. Mon. 49 (1942), 286-295. | DOI | MR | JFM
[27] McCoy, N. H.: Annihilators in polynomial rings. Am. Math. Mon. 64 (1957), 28-29. | DOI | MR | JFM
[28] Paykan, K.: Nilpotent elements of skew Hurwitz series rings. Rend. Circ. Mat. Palermo (2) 65 (2016), 451-458. | DOI | MR | JFM
[29] Paykan, K.: A study on skew Hurwitz series rings. Ric. Mat. 66 (2017), 383-393. | DOI | MR | JFM
[30] Paykan, K.: Principally quasi-Baer skew Hurwitz series rings. Bull. Unione Mat. Ital. 10 (2017), 607-616. | DOI | MR | JFM
[31] Rege, M. B., Chhawchharia, S.: Armendariz rings. Proc. Japan Acad., Ser. A 73 (1997), 14-17. | DOI | MR | JFM
[32] Sharma, R. K., Singh, A. B.: Unified extensions of strongly reversible rings and links with other classic ring theoretic properties. J. Indian Math. Soc., New Ser. 85 (2018), 434-448. | DOI | MR | JFM
[33] Sharma, R. K., Singh, A. B.: Zip property of skew Hurwitz series rings and modules. Serdica Math. J. 45 (2019), 35-54. | MR
[34] Sharma, R. K., Singh, A. B.: Skew Hurwitz series rings and modules with Beachy-Blair conditions. Kragujevac J. Math. 47 (2023), 511-521. | DOI | MR
[35] Singh, A. B., Dixit, V. N.: Unification of extensions of zip rings. Acta Univ. Sapientiae, Math. 4 (2012), 168-181. | MR | JFM
[36] Stenström, B.: Rings of Quotients: An Introduction to Methods of Ring Theory. Die Grundlehren der mathematischen Wissenschaften 217. Springer, Berlin (1975). | DOI | MR | JFM
[37] Taft, E. J.: Hurwitz invertibility of linearly recursive sequences. Combinatorics, Graph Theory, and Computing Congressus Numerantium 73. Utilitas Mathematica, Winnipeg (1990), 37-40. | MR | JFM
[38] Tominaga, H.: On $s$-unital rings. Math. J. Okayama Univ. 18 (1976), 117-134. | MR | JFM
[39] Zelmanowitz, J. M.: The finite intersection property on annihilator right ideals. Proc. Am. Math. Soc. 57 (1976), 213-216. | DOI | MR | JFM
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