BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION

In this paper, we characterize the bi-Amalgamations of small weak global dimension. The new results compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations

___

  • [1] K. Alaoui Ismaili and N. Mahdou, Coherence in amalgamated algebra along an
  • ideal, Bull. Iranian Math. Soc., 41(3) (2015), 625-632.
  • [2] S. Bazzoni and S. Glaz, Pr¨ufer rings, in: J. Brewer, S. Glaz, W. Heinzer,
  • B. Olberding (Eds.), Multiplicative ideal theory in commutative algebra: A
  • tribute to the work of Robert Gilmer, Springer, New York, (2006), 55–72.
  • [3] M. B. Boisen, Jr. and P. B. Sheldon, CPI-extensions: overrings of integral
  • domains with special prime spectrum, Canad. J. Math., 29(4) (1977), 722-737.
  • [4] M. Chhiti, M. Jarrar, S. Kabbaj and N. Mahdou, Pr¨ufer conditions in an amalgamated
  • duplication of a ring along an ideal, Comm. Algebra, 43(1) (2015),249-261.
  • [5] M. D’Anna and M. Fontana, The amalgamated duplication of a ring along a
  • [6] M. D’Anna and M. Fontana, An amalgamated duplication of a ring along an
  • [7] M. D’Anna, C. A. Finacchiaro and M. Fontana, Amalgamated algebras along
  • an ideal, Commutative algebra and its applications, Walter de Gruyter, Berlin,(2009), 155–172.
  • [9] L. Fuchs, Uber die ideale arithmetischer ringe, Comment. Math. Helv., 23(1949), 334-341.
  • [10] S. Glaz, Commutative Coherent Rings, Lecture Notes in Math., 1371, SpringerVerlag,Berlin, 1989.
  • [11] S. Greco and P. Salmon, Topics in m-Adic Topologies, Springer-Verlag, Berlin,Heidelberg, 1971.
  • [12] C. U. Jensen, Arithmetical rings, Acta Math. Acad. Sci. Hungar., 17 (1966),115-123.
  • [8] M. D’Anna, C. A. Finacchiaro and M. Fontana, Properties of chains of prime
  • ideals in an amalgamated algebra along an ideal, J. Pure Appl. Algebra, 214(9)
  • (2010), 1633–1641.