Global dimension of rings of functions

References

• Arkhangelski[icaron] , A.V. 1978 . Structure and classification of topological spaces and cardinal invariants . Russian Math. Surveys , 33:6 : 33 – 96 .
   Google Scholar
• Atiyah , M.F. and MacDonald , I.G. 1969 . Introduction to Commutative Algebra , Reading, Mass : Addison-Wesley .
   Google Scholar
• Auslander , M. 1955 . On the dimension of module and algebras, III:Global dimension . Nagoya Math. J , 9 : 67 – 77 .
   Google Scholar
• Blair , R.L. 1976 . Spaces in which special sets are z-embedded . Canadian J. Math , 28 : 673 – 690 .
   Web of Science ®Google Scholar
• Brookshear , J.G. 1978 . On projective prime ideal in C(X) . Proc. AMS , 69 : 203 – 204 .
   Web of Science ®Google Scholar
• Comfort , W.W. and Negrepontis , K.S. 1982 . “ Chain Conditions in Topology ” . In Cambridge Tracts in Math Vol. 79 , Cambridge, New York London
   Google Scholar
• De Marco , G. 1983 . “ Projectivity of pure ideals ” . In Rend. Sem. Mat , Vol. 68 , 289 – 304 . Univ. Padova .
   Google Scholar
• Efimov , B.A. 1970 . Extremally disconnected compact spaces and absolutes . Transl. Moscow Math. Soc , 23 : 243 – 285 .
   Google Scholar
• Engelking , R. 1977 . General Topology. Mon. Mat , Vol. 60 , Warsaw : Polish Scientific Publishers .
   Google Scholar
• Finn , R.T. . Reflections on the global dimension of rings of continuous functions. Survey article . Proceedings Conference on Ordered Algebraic Structures . 1995 , Curagao. Edited by: Charles Holland , W. and Martinez , J. pp. 27 – 42 . Kluwer Academic Publishers .
   Google Scholar
• Finn , R.T. August 1997 . Homological features of rings of Continuous Functions , August , University of Florida Doctoral Dissertation .
   Google Scholar
• Finn , R.T. , Martinez , J. and Mcgovern , W.W. 1997 . The global dimension of an f-ring via its space of minimal prime ideals . Comm.in Algebra , 25 ( 3 ) August : 905 – 921 .
   Web of Science ®Google Scholar
• Finn , R.T. , Martinez , J. and McGovern , W.W. . Finite separation spaces . Proceedings Conf. on Topology & Topological Groups . Curasao. Topology & Appl .
   Google Scholar
• Gillman , L. and Henriksen , M. 1956 . Rings of continuous functions in which every finitely generated ideal is principal . Trans. AMS , 82 ( 3 ) August : 366 – 391 .
   Google Scholar
• Gillman , L. and Jerison , M. 1976 . Rings of Continuous Functions , Vol. GTM 43 , New York : Springer Verlag . Heidelberg,Berlin
   Google Scholar
• Glaz , S. 1989 . “ Commutative Coherent Rings ” . In Lecture Notes in Math , Vol. 1371 , Berlin : Springer Verlag . Heidelberg,New York
   Google Scholar
• Hager , A.W. and Martinez , J. 1993 . Fraction-dense algebras and spaces . Canadian J. Math , 45 ( 5 ) : 977 – 996 .
   Web of Science ®Google Scholar
• Hausdorff , F. 1936 . Über zwei Sä;tze von G., Fichtenholz und L. Kantorovich . Studia Math , 6 ( 5 ) : 18 – 19 .
   Google Scholar
• Henriksen , M. , Isbell , J.R. and Johnson , D.G. 1961 . Residue class fields of lattice-ordered algebras . Fund. Math , 50 ( 5 ) : 107 – 117 .
   Google Scholar
• Kaplansky , I. 1958 . Projective modules . Ann. of Math , 68 ( 5 ) : 372 – 377 .
   Web of Science ®Google Scholar
• Kislyakov , S.V. 1973 . Free subalgebras of complete boolean algebras and spaces of continuous functions . Siberian Math. Jour , 14 ( 5 ) : 395 – 403 .
   Google Scholar
• Kohls , C.W. 1958 . Prime ideals in rings of continuous functions . Illinois J. Math , 2 ( 5 ) : 505 – 536 .
   Google Scholar
• Donald Monk , J. 1989 . Handbook of Boolean Algebras , Amsterdam, New York : North Holland . Tokyo
   Google Scholar
• Kunen , K. 1980 . “ Set Theory ” . In Studies in Logic , Vol. 102 , Amsterdam : North Holland . Amsterdam-New York-Oxford-Tokyo
   Google Scholar
• Martinez , J. 1995 . The maximal ring of quotients of a f-ring , Vol. 33 , 335 – 369 . Algebra Univ .
   Google Scholar
• Martinez , J. and Woodward , S. 1992 . Bézout and Prüfer f-rings . Comm. in Alg , 20 ( 10 ) : 2975 – 2989 .
   Web of Science ®Google Scholar
• Donald Monk , J. 1990 . “ Cardinal Functions on Boolean Algebras ” . In Lectures in Math , Basel : Birkhäuser Verlag . Boston,Berlin
   Google Scholar
• Neville , C.W. 1989 . Flat C(X)-modules and F-spaces . Math. Proc. Camb. Phil. Soc , 106 : 237 – 244 .
   Google Scholar
• Osofsky , B.L. 1967 . Global dimension of valuation rings . Trans. AMS , 127 : 136 – 149 .
   Web of Science ®Google Scholar
• Osofsky , B.L. . Homological Dimensions on Modules . CBMS Reg. Conf. Series in Math . Vol. 12 , Providence, RI : American Mathematical Society .
   Google Scholar
• Pierce , R.S. 1958 . A note on complete Boolean algebras . Proc. AMS , 9 : 892 – 896 .
   Google Scholar
• Porter , J.R. and Woods , R.G. 1989 . Extensions an Absolutes of Hausdorff Spaces , New York : Springer Verlag . Berlin,Heidelberg
   Google Scholar
• Rotman , J.J. 1979 . “ An Introduction to Homological Algebra ” . In Pure & Appl. Math , Vol. 85 , Boston : Academic Press . San Diego,London
   Google Scholar
• Večtomov , E.M. 1981 . On ideals of rings of continuous functions . Mathematika, Izvestia Vyschik Uchebnyk Zavedenii , 224 ( 1 ) : 3 – 10 . In Russian
   Google Scholar
• Walker , R.C. 1974 . “ The Stone-Čech Compactification ” . In Ergebn. Math , Vol. 83 , Berlin : Springer Verlag . Heidelberg,New York
   Google Scholar