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Original Articles

Maximal and minimal prime ideals of incidence algebras

Pages 1823-1840 | Received 01 Sep 1995, Published online: 27 Jun 2007

References

  • Balbes , R. and Dwinger , P. 1974 . “Distributive Lattices,” . Columbia, Missouri : Univ. of Missouri Press .
  • Comfort , W. W. and Negrepontis , S. 1974 . “The Theory of Ultrafilters,” . New York : Springer‐Verlag .
  • Doubliet , P. , Rota , G‐ C. and Stanley , R. 1972 . On the foundation of combinatorial theory, VI: The idea of a generating function . Proc. 6th Berkeley Symp. on Math. Stat. and Prob , II : 267 – 318 .
  • Farkas , D. R. 1974 . Radicals and primes in incidence algebras . Discrete Math , 10 : 257 – 268 .
  • Gilmer , R. and Heinzer , W. 1992 . Products of commutative rings with zero‐dimensionality . Trans. Amer. Math. Soc , 331 : 663 – 680 .
  • Jacobson , N. 1980 . “Basic Algebra II,” . San Francisco : W.H. Freeman and Co .
  • Kaplansky , I. 1970 . “Commutative Rings” . Boston : Allyn and Bacon, Inc .
  • Lambek , J. 1966 . “Lectures on Rings and Modules,” . Waltham, Massachusetts : Blaisdell Pub. Co .
  • Maroscia , P. 1974 . Sur les anneaux de dimension zero . Atti Accad. Naz. Lincer Rend Cl. Sci. Fis. Mat. Natur , 56 : 451 – 459 .
  • Nachbin , L. 1947 . Une propriete caracteristique des algebres booleiennes . Port. Math. , 6 : 115 – 118 .
  • O'DONNELL , C. J. 1992 . “ Maximal and Minimal Prime Ideals of Incidence Algebras with Applications to Ring Theory ” . The University of Connecticut . Ph.D.Thesis
  • O' Donnell , C. J. 1994 . Prime ideals in the product of commutative rings with identity . Comm.. Alg. , 22 ( 8 ) : 3061 – 3086 .
  • Pierce , R. S. 1961 . Rings of integer‐valued continuous functions . Trans. Amer. Math. Soc , 100 ( 8 ) : 371 – 394 .
  • Rota , G. ‐C. 1964 . On the foundations of combinatorial theory I: Theory of M öbius functions . Z. Wahr Scheinlichkeits Theorie und Verw. Gebiete , 2 ( 8 ) : 340 – 368 .
  • Spiegel , E. 1994 . Radicals of incidence algebras . Comm. Alg , 22 ( 1 ) : 139 – 149 .
  • Schmerl , J. H. and Spiegel , E. 1991 . Prime ideals in incidence algebras . Comm. Alg , 19 ( 11 ) : 3011 – 3040 .
  • Van Wyk , L. 1988 . Maximal left ideals in structural matrix rings . Comm, Alg , 16 ( 2 ) : 399 – 419 .

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