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Original Articles

Some Pólya-Type Irreducibility Criteria for Multivariate Polynomials

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Pages 3733-3744 | Received 16 Apr 2011, Published online: 11 Sep 2012

REFERENCES

  • Ayad , M. ( 2004 ). Irreducibility of f(u(x), v(y)) . J. Algebra 279 : 302 – 307 .
  • Bilu , Y. F. ( 1999 ). Quadratic factors of f(x) − g(y) . Acta Arith. 90 ( 4 ): 341 – 355 .
  • Bilu , Y. F. , Tichy , R. F. ( 2000 ). The Diophantine equation f(x) = g(y) . Acta Arith. 95 ( 3 ): 261 – 288 .
  • Bonciocat , A. I. , Bonciocat , N. C. ( 2006 ). Some classes of irreducible polynomials . Acta Arith. 123 ( 4 ): 349 – 360 .
  • Bonciocat , A. I. , Bonciocat , N. C. ( 2008 ). A Capelli type theorem for multiplicative convolutions of polynomials . Math. Nachr. 281 ( 9 ): 1240 – 1253 .
  • Bonciocat , A. I. , Zaharescu , A. ( 2005 ). Irreducibility results for compositions of polynomials in several variables . Proc. Indian Acad. Sci. (ath. Sci.) 115 ( 2 ): 117 – 126 .
  • Bonciocat , N. C. ( 2010 ). On an irreducibility criterion of Perron for multivariate polynomials . Bull. Math. Soc. Sci. Math. Roumanie 53 ( 101)(3 ): 213 – 217 .
  • Bonciocat , N. C. , Zaharescu , A. (2008). Irreducible multivariate polynomials obtained from polynomials in fewer variables. J. Pure Appl. Algebra 212:2338–2343.
  • Cavachi , M. , Vâjâitu , M. , Zaharescu , A. ( 2004 ). An irreducibility criterion for polynomials in several variables . Acta Math. Univ. Ostrav. 12 ( 1 ): 13 – 18 .
  • Dorwart , H. L. , Ore , O. ( 1933 ). Criteria for the irreducibility of polynomials . Ann. of Math. 34 : 81 – 99 .
  • Dorwart , H. L. , Ore , O. ( 1934 ). Criteria for the irreducibility of polynomials . Ann. of Math. 35 : 195 .
  • Gyory , K. , Hajdu , L. , Tijdeman , R. ( 2011 ). Irreducibility criteria of Schur-type and Pólya-type . Monatsh. Math. 163 ( 4 ): 415 – 443 .
  • Lang , S. ( 2002 ). Algebra . Graduate Texts in Mathematics 211. Berlin , New York : Springer .
  • MacLane , S. ( 1936 ). A construction for absolute values in polynomial rings . Trans. Amer. Math. Soc. 40 : 363 – 395 .
  • MacLane , S. The Schönemann - Eisenstein irreducibility criteria in terms of prime ideals . Trans. Amer. Math. Soc. 43 : 226 – 239 .
  • Panaitopol , L. , \c Stef\u anescu, D. ( 1990 ). On the generalized difference polynomials . Pacific J. Math. 143 ( 2 ): 341 – 347 .
  • Perron , O. ( 1907 ). Neue Kriterien für die Irreduzibilität algebraischer Gleichungen . J. Reine Angew. Math. 132 : 288 – 307 .
  • Pólya , G. ( 1919 ). Verschiedene Bemerkungen zur Zahlentheorie . Jahresber. Deutschen Math. Ver. 28 : 31 – 40 .
  • Rubel , L. A. , Schinzel , A. , Tverberg , H. ( 1980 ). On difference polynomials and hereditarily irreducible polynomials . J. Number Theory 12 : 230 – 235 .
  • Schinzel , A. ( 2000 ). Polynomials with Special Regard to Reducibility. Encyclopedia Math. Appl. 77. Cambridge Univ. Press .
  • Schur , I. ( 1908 ). Problem 226 . Archiv. der Math. und Physik 13 ( 3 ): 367 .
  • Shanok , C. ( 1936 ). Convex polyhedra and criteria for irreducibility . Duke Math. J. 2 : 103 – 111 .
  • Communicated by T. Albu.

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