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Nil Armendariz rings of Hurwitz series type 1 | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 8، دوره 16، شماره 9، آذر 2025، صفحه 87-93 اصل مقاله (344.43 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.35416.5275 | ||
| نویسندگان | ||
| Kianoosh Sabzipour1؛ Hamid Haj Seyyed Javadi* 2 | ||
| 1Department of Pure Mathematics, Tarbiat Modares University, Tehran, Iran | ||
| 2Department of Mathematics and Computer Science, Shahed University, Tehran, Iran | ||
| تاریخ دریافت: 02 مرداد 1403، تاریخ پذیرش: 06 مهر 1403 | ||
| چکیده | ||
| In this paper, we study the structure of the set of nilpotent elements in Armendariz rings of Hurwitz series type and introduce nil Armendariz as a generalization. It is proved that a ring $R$ is nil Armendariz of Hurwitz series type if and only if $R$ has characteristic zero and $Nil(R)$ is an ideal. We provide many examples of nil Armendariz rings of Hurwitz series type and extend the class of nil Armendariz rings of Hurwitz series type through various ring extensions. | ||
| کلیدواژهها | ||
| nil Armendariz ring؛ nil Armendariz ring of Hurwitz series type؛ nil Armendariz ring of skew Hurwitz series type | ||
| مراجع | ||
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[1] A. Amitsur, Algebras over infinite fields, Proc. Amer. Math. Soc. 7 (1956), 35–48. [2] D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265–2272. [3] R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra 319 (2008), 3128–3140. [4] E.P. Armendariz, A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc. textbf18 (1974), 470–473. [5] A. Benhissi, Ideal structure of Hurwitz series rings, Contrib. Algebra Geom. 47 (2007), no. 1, 251–256. [6] G.F. Birkenmeier, J.Y. Kim, and J.K. Park, On polynomial extensions of principally quasi-Baer rings, Kyungpook Math. J. 40 (2000), 247–253. [7] G.F. Birkenmeier, J.Y. Kim, and J.K. Park, Quasi-Baer ring extensions and biregular rings, Bull. Aust. Math. Soc. 61 (2000), 39–52. [8] G.F. Birkenmeier, J.Y. Kim, and J.K. Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001), no. 2, 639–660. [9] G. F. Birkenmeier, J.Y. Kim, J.K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001), 24–42. [10] W.E. Clark, Twisted matrix units semigroup algebra, Duke Math. J. 34 (1967), 417–424. [11] C. Faith, Rings with zero intersection property on annihilators Zip rings, Publ. Mat. 33 (1989), 329–332. [12] C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751–761. [13] I. Kaplansky, Rings of Operators, New York: Benjamin, 1965. [14] W.F. Keigher, Adjunctions and comonads in differential algebra, Pacific J. Math 56 (1975), 99–112. [15] W.F. Keigher, On the ring of Hurwitz series, Comm. Algebra 25 (1997), no. 6, 1845–1859. [16] W.F. Keigher and F.L. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra 146 (2000), 291–304. [17] L. Liang, L, Wang, and Z. Ziu, On a generalization of semi commutative rings, Taiwanese J. Math. 11 (2007), no. 5, 1359–1368. [18] Z. Liu and R. Zhao, On weak Armendariz rings, Comm. Algebra 34 (2006), 2607–2616. [19] P. Pollingher and A. Zaks, On Baer and quasi-Baer rings, Duke Math. J. 37 (1970), 127–138. [20] M.B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci, 73 (1997), 14–17. [21] A. Smoktunowicz, Polynomial rings over nil rings need not be nil, J. Algebra 233 (2000), 427–436. [22] J.M. Zelmanowitz, The finite intersection property on annihilator right ideals, Proc. Amer. Math. Soc. 57 (1976), 213–216 | ||
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