Research & Publications

Research interests:

Commutative Ring Theory
Coding Theory

Research projects:

Some algebraic aspects of the formal power series ring and applications (Principal Investigator, Grant No. 101.04-2019.06), National Foundation for Science & Technology Development (NAFOSTED), from 09/2019 to 09/2021 (Ongoing).
Some algorithms in commutative rings with applications in finding solutions of algebraic ODEs and bounds of codes (Principal Investigator, Grant FOSTECT.2017.BR.02), Foundation for Science and Technology Development of Ton Duc Thang University (FOSTECT), from 01/2018 to 07/2019 (Finished).

Publications:

2021:

[28] L.T.N. Giau, P.T. Toan, and T.N. Vo, Dedekind–Mertens Lemma for Power Series in an Arbitrary Set of Indeterminates, Vietnam Journal of Mathematics (2021).

[27] G.W. Chang and P.T. Toan, Subrings of the power series ring over a principal ideal domain, Communications in Algebra 49 (2021), no. 9, 3748-3759. (ISI)

[26] G.W. Chang and P.T. Toan, Twisted Polynomial and Power Series Rings, Bulletin of the Iranian Mathematical Society (2021). (ISI)

[25] P.T. Toan and B.G. Kang, Chains of prime ideals in power series rings, Journal of Pure and Applied Algebra 225 (2021), no. 11, 106726.

[24]. T.N. Vo, M. Razzaghi, and P.T. Toan, A numerical method for solving variable-order fractional diffusion equations using fractional-order Taylor wavelets, Numerical Methods for Partial Differential Equations 37 (2021), no. 3, 2668–2686. (ISI)

[23]. P.T. Toan, T.N. Vo, and M. Razzaghi, Taylor wavelet method for fractional delay differential equations, Engineering with Computers 37 (2021), no. 1, 231–240. (ISI)

2020:

[22] G.W. Chang and P.T. Toan, Polynomial and power series ring extensions from sequences, Journal of Algebra and its Applications (2020). (ISI)

[21]. P.T. Toan and B.G. Kang, Krull dimension of power series rings, Journal of Algebra 562 (2020), 306-322. (ISI)

[20]. L.T.N. Giau, B.G. Kang, and P.T. Toan, On the generalized Krull property in power series rings, Journal of Pure and Applied Algebra 224 (2020), no. 11, 106409. (ISI)

2019:

[19]. T.N. Vo and P.T. Toan, The power series Dedekind-Mertens number, Comm. Algebra 47 (2019), no. 9, 3481-3489. (ISI)

[18]. L.T.N. Giau and P.T. Toan, A simple proof of the improved Johnson bound for binary codes, Bull. Korean Math. Soc. 56 (2019), no. 2, 391-397. (ISI)

[17]. P.T. Toan and B.G. Kang, Krull dimension of a power series ring over a valuation domain, J. Algebra 519 (2019), 62-86. (ISI)

2018:

[16]. P.T. Toan, H.K. Kim, and J. Kim, Improved linear programming bound on sizes of doubly constant-weight codes, Finite Fields Th. App. 54 (2018), 230-252. (ISI)

[15]. L.T.N. Giau and P.T. Toan, On generalized Krull power series rings, Bull. Korean Math. Soc. 55 (2018), no. 4, 1007-1012. (ISI)

[14]. L.T.N. Giau and P.T. Toan, Krull dimension of Hurwitz polynomial rings over Pr\"ufer domains, Bull. Korean Math. Soc. 55 (2018), no. 2, 625-631. (ISI)

[13]. M.H. Park, B.G. Kang, and P.T. Toan, Dedekind–Mertens lemma and content formulas in power series rings, J. Pure Appl. Algebra 222 (2018), no. 8, 2299-2309. (ISI)

[12]. L.T.N. Giau and P.T. Toan, On power series rings over valuation domains, Comm. Algebra 46 (2018), no. 5, 1843-1853. (ISI)

[11]. L.T.N. Giau and P.T. Toan, Transcendental degree in power series rings, J. Algebra 501 (2018), 51-67. (ISI)

[10]. P.T. Toan and B.G. Kang, Krull dimension of power series rings over non-SFT domains, J. Algebra 499 (2018), 516-537. (ISI)

2017:

[9]. P.T. Toan and B.G. Kang, Krull dimension and unique factorization in Hurwitz polynomial rings, Rocky Mountain J. Math. 47 (2017), no. 4, 1317-1332. (ISI)

2016:

[8]. B.G. Kang and P.T. Toan, A remark on the Noetherian property of power series rings, Pacific J. Math. 283 (2016), no. 2, 353–363. (ISI)

2015:

[7]. G.W. Chang, B.G. Kang, and P.T. Toan, The Krull dimension of power series rings over almost Dedekind domains, J. Algebra 438 (2015), 170-187. (ISI)

[6]. B.G. Kang and P.T. Toan, Noetherian property of subrings of power series rings II, J. Pure Appl. Algebra 219 (2015), no. 9, 4055–4060. (ISI)

[5]. B.G. Kang and P.T. Toan, Noetherian property of subrings of power series rings, Comm. Algebra 43 (2015), no. 2, 440–446. (ISI)

2014:

[4]. H.K. Kim and P.T. Toan, New inequalities for q-ary constant-weight codes, Des. Codes Cryptogr. 73 (2014), no. 2, 369–381. (ISI)

2013:

[3]. H.K. Kim and P.T. Toan, Improved semidefinite programming bound on sizes of codes, IEEE Trans. Inform. Theory 59 (2013), no. 11, 7337–7345. (ISI)

[2]. B.G. Kang, K.A. Loper, T.G. Lucas, M.H. Park, and P.T. Toan, The Krull dimension of power series rings over non-SFT rings, J. Pure Appl. Algebra 217 (2013), no. 2, 254–258. (ISI)

2012:

[1]. B.G. Kang, H.K. Kim, and P.T. Toan, Delsarte's linear programming bound for constant-weight codes, IEEE Trans. Inform. Theory 58 (2012), no. 9, 5956–5962. (ISI)

Updated: May 2021

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