Abstract
In this article, we shall discuss pullback diagrams of the following type:
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References
D.F. Anderson and D. Dobbs, Pairs of rings with the same prime ideals, Can. J. Math. 32 (1980), 362–384.
D.F. Anderson and A. Ryckaert, The class group of D + M, J. Pure Appl. Algebra 52 (1988), 199–212.
E. Bastida and R. Gilmer, Overrings and divisorial ideals of the form D+M, Michigan Math. J. 20 (1973), 79–95.
M. Boisen and P. Sheldon, CPI-extensions: overrings of integral domains with special prime spectrum, Can. J. Math. 24 (1977), 722–737.
J. Brewer and E. Rutter, D+M constructions with general overrings, Michigan Math. J. 23 (1976), 33–41.
P.-J. Cahen, Couples d’anneaux partageant un idéal, Arch. Math. 51 (1988), 505–514.
P.-J. Cahen, Construction B, I, D et anneaux localement ou residuellement de Jaffard, Arch. Math. 54 (1990), 125–141.
D. Costa, J. Mott, and M. Zafrullah, The construction D + XD X [X], J. Algebra 53 (1978), 423–439.
D. Dobbs, E. Houston, T. Lucas, and M. Zafrullah, t-linked overrings and Prüfer v-multiplication domains, Comm. Algebra 17 (1989), 2835–2852.
D. Dobbs and I. Papick, When is D + M coherent, Proc. Amer. Math. Soc. 56 (1976), 51–54.
M. Fontana, Topologically defined classes of commutative rings, Ann. Mat. Pura Appl. 123 (1980), 331–355.
M. Font ana and S. Gabelli, On the class group and the local class group of a pullback, J. Algebra 181 (1996), 803–835.
M. Fontana and S. Gabelli, Prüfer domains with class group generated by the classes of the invertible maximal ideals, Comm. Algebra 25 (1997), 3993–008.
M. Fontana, S. Gabelli, and E. Houston, UMT-domains and domains with Prüfer integral closure, Comm. Algebra 26 (1998), 1017–1039.
M. Fontana, J. Huckaba, and I. Papick, Prüfer domains, Dekker, New York, 1977.
S. Gabelli and E. Houston, Coherentlike conditions in pullbacks, Michigan Math. J. 44 (1997), 99–123.
R. Gilmer, Multiplicative ideal theory, Queen’s Papers on Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ontario, 1968.
R. Gilmer, Multiplicative ideal theory, Dekker, New York, 1972.
R. Gilmer and W. Heinzer, On the number of genearators of an invertible ideal, J. Algebra 14 (1970), 139–151.
J. Hedstrom and E. Houston, Pseudo-valuation domains, Pacific J. Math. 75 (1978), 137–147.
R. Heitmann, Generating ideals in Prüfer domains, Pacific J. Math. 62 (1976), 117–126.
P. Jaffard, Les systems d’idéaux, Dunod, Paris, 1960.
A. Mimouni, Coherent-like properties in pullbacks, in Advances in commutative ring theory, Lecture Notes in Pure and Applied Mathematics 205, pp. 437–459, Dekker, New York, 1999.
A. Seidenberg, On the dimension theory of rings II, Pacific J. Math. 4 (1954), 603–614.
H. Schülting, Über die Erzengendenanzahl invertier barer Ideale in Prüferringen, Comm. Algebra 7 (1979), 1331–1349.
R. Swan, n-generator ideals in Prüfer domains, Pacific J. Math. 111 (1984), 433–446.
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Gabelli, S., Houston, E. (2000). Ideal Theory in Pullbacks. In: Chapman, S.T., Glaz, S. (eds) Non-Noetherian Commutative Ring Theory. Mathematics and Its Applications, vol 520. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3180-4_9
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DOI: https://doi.org/10.1007/978-1-4757-3180-4_9
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