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Junchao Wei and Zhiyong Fan

References 1. Ligh, S.; Richoux, A. - A commutativity theorem for rings, Bull. Austral. Math. Soc., 16 (1977), 75-77. 2. Pinter-Lucke, J. - Commutativity conditions for rings: 1950-2005, Expo. Math., 25 (2007), 165-174.

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Ivan Chajda and Helmut Länger

. Chajda and H. Länger, When does a semiring become a residuated lattice ?, Asian-Eur. J. Math. 9 (2016) 1650088 (10 pages). doi:10.1142/S1793557116500881 [6] R.P. Dilworth, Non-commutative residuated lattices , Trans. Amer. Math. Soc. 46 (1939) 426–444. doi:10.2307/1989931 . [7] N. Galatos, P. Jipsen, T. Kowalski and H. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics (Elsevier, Amsterdam, 2007). ISBN 978-0-444-52141-5. [8] J.S. Golan, The Theory of Semirings with Applications in

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Hidayet Huda Kosal and Murat Tosun

. Jiang and S. Ling, On a solution of the quaternion matrix equa- tion AeX - XB = C and its applications, Adv. Appl. Clifford Algebras 23 (2013), 689-699. [10] C. Segre, The real representations of complex elements and extension tobicomplex, Systems. Math. Ann. 40 (1892), 40: 413. [11] F. Catoni, R. Cannata and P. Zampetti, An introduction to commutative quaternions, Adv. Appl. Clifford Algebras 16 (2006), 1-28. [12] S. C. Pei, J. H. Chang and J. J. Ding, Commutative reduced bi-quaternions and their fourier transform for

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Dariusz Dudzik and Marcin Skrzynski

References [1] Atiyah M.F., MacDonald I.G., Introduction to Commutative Algebra, Addison-Wesley Publishing Company, Reading, 1969. [2] Dudzik D., Skrzynski M., An outer measure on a commutative ring, Algebra Discrete Math. 21 (2016), no. 1, 51-58. [3] Federer H., Geometric Measure Theory, Springer, Berlin, 1969. [4] Halmos P.R., Measure Theory, Springer, New York, 1976.

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S. A. Plaksa and R. P. Pukhtaievych

, arXiv: math/0101200v1 [math.CV], 24 Jan 2001. [6] D. A. Pinotsis, Commutative quaternions, spectral analysis and boundary value problems , Complex Variables and Elliptic Equations, 57(9)(2012), 953 – 966. [7] A. K. Bakhtin, A generalization of some results in the theory of univa-lent functions on a multi-dimensional complex space , Dop. NAN Ukr., (3)(2011), 7 – 11 [in Russian]. [8] P. W. Ketchum, Analytic functions of hypercomplex variables , Trans. Amer. Math. Soc., 30(4)(1928), 641 – 667. [9] I.P. Mel'nichenko, The representation of harmonic mappings by

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Zahra Barati and Mojgan Afkhami

R eferences [1] M. Afkhami, When the comaximal and zero-divisor graphs are ring graphs and outerplanar , Rocky Mountain J. Math. 6 (2014) 1745–1761. doi:10.1216/RMJ-2014-44-6-1745 [2] M. Afkhami and K. Khashyarmanesh, The cozero-divisor graph of a commutative ring , Southeast Asian Bull. Math. 35 (2011) 753–762. [3] M. Afkhami and K. Khashyarmanesh, On the cozero-divisor graphs of commutative rings and their complements , Bull. Malays. Math. Sci. Soc. 35 (2012) 935–944. [4] M. Afkhami and K. Khashyarmanesh, Planar, outerplanar

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Roman Pukhtaievych and Sergiy Plaksa

theory of analytic function in normed abelian vector rings, Trans. Amer. Math. Soc., 54, 1943, pp. 414-425. [14] Plaksa S.A. and Pukhtaievych R.P. Constructive description of monogenic functions in a three-dimensional harmonic algebra with one- dimensional radical, Ukr. Math. J., 65(5), 2013, pp. 740-751. [15] Shpakivskyi V.S. Constructive description of monogenic functions in a finite-dimensional commutative associative algebra, Adv. Pure Appl. Math., 7(1), 2016, pp. 63-75. [16] Pukhtaievych R.P. Power series and Laurent

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Lilya Budaghyan and Tor Helleseth

. Inform. Theory 52 (2006), 1141-1152. [11] BUDAGHYAN, L.-HELLESETH, T.: New perfect nonlinear multinomials over F p 2 k for any odd prime p, in: Proc. of Internat. Conference on Sequences and Their Applications-SETA ’08, Lecture Notes in Comput. Sci., Vol. 5203, Springer-Verlag, Berlin, 2008, pp. 401-414. [12] BUDAGHYAN, L.-HELLESETH, T.: New commutative semifields defined by new PN multinomials, Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences, 2010 (to appear). [13] CARLET, C

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Shahabaddin Ebrahimi Atani and Fatemeh Esmaeili Khalil Saraei

References [1] D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra, 159 (1993), 500-514. [2] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra, 320 (2008), 2706-2719. [3] D. F. Anderson and P. F. Livingston, The zero-divisor graph of a com- mutative ring, J. Algebra, 217 (1999), 437-447. [4] P. J. Allen, A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21 (1969), 412-416. [5] I. Beck

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B. Ramoorthy Reddy and C. Jaya Subba Reddy

R eferences [1] M. Ashraf and N.U. Rehman, On commutativity of rings with derivations , Result. Math. 42 (2002) 03–08. [2] M. Ashraf and N.U. Rehman, On derivation and commutativity in prime rings , East-West J. Math. 3 (2001) 87–91. [3] M. Atteya and D. Resan, Commuting derivations of semiprime rings , Int. J. Math. Sci. 6 (2011) 1151–1158. [4] H.E. Bell and M.N. Daif, On derivations and commutativity in prime rings , Acta Math. Hungar. 66 (1995) 337–343. [5] H.E. Bell and W.S. Martindale, Centralizing mappings of