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BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION

Year 2017, Volume: 21 Issue: 21, 127 - 136, 17.01.2017
https://doi.org/10.24330/ieja.296160

Abstract

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

References

  • [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.
Year 2017, Volume: 21 Issue: 21, 127 - 136, 17.01.2017
https://doi.org/10.24330/ieja.296160

Abstract

References

  • [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.
There are 20 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Articles
Authors

Mohammed Tamekkante This is me

El Mehdi Bouba This is me

Publication Date January 17, 2017
Published in Issue Year 2017 Volume: 21 Issue: 21

Cite

APA Tamekkante, M., & Bouba, E. M. (2017). BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION. International Electronic Journal of Algebra, 21(21), 127-136. https://doi.org/10.24330/ieja.296160
AMA Tamekkante M, Bouba EM. BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION. IEJA. January 2017;21(21):127-136. doi:10.24330/ieja.296160
Chicago Tamekkante, Mohammed, and El Mehdi Bouba. “BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION”. International Electronic Journal of Algebra 21, no. 21 (January 2017): 127-36. https://doi.org/10.24330/ieja.296160.
EndNote Tamekkante M, Bouba EM (January 1, 2017) BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION. International Electronic Journal of Algebra 21 21 127–136.
IEEE M. Tamekkante and E. M. Bouba, “BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION”, IEJA, vol. 21, no. 21, pp. 127–136, 2017, doi: 10.24330/ieja.296160.
ISNAD Tamekkante, Mohammed - Bouba, El Mehdi. “BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION”. International Electronic Journal of Algebra 21/21 (January 2017), 127-136. https://doi.org/10.24330/ieja.296160.
JAMA Tamekkante M, Bouba EM. BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION. IEJA. 2017;21:127–136.
MLA Tamekkante, Mohammed and El Mehdi Bouba. “BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION”. International Electronic Journal of Algebra, vol. 21, no. 21, 2017, pp. 127-36, doi:10.24330/ieja.296160.
Vancouver Tamekkante M, Bouba EM. BI-AMALGAMATION OF SMALL WEAK GLOBAL DIMENSION. IEJA. 2017;21(21):127-36.