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Armendariz-like properties in bi-amalgamations

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Abstract

This paper examines the transfer of the Armendariz (resp., weak Armendariz, resp., nil-Armendariz) property to bi-amalgamations. Our results cover previously known results on amalgamations, and provide the construction of various and original examples satisfying the above-mentioned properties.

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References

  1. Anderson, D., Camillo, V.: Armendariz rings and Gaussian rings. Comm. Algebra 26(7), 2265–2272 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. D’Anna, M., Finacchiaro, C.A., Fontana, M.: Amalgamated algebras along an ideal. Comm. Algebra Appl. pp. 241–252. (2009)

  3. Antoine, R.: Nilpotent elements and Armendariz rings. J. Algebra 319, 3128–3140 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Armendariz, E., Chhawchharia, S.: A note on extensions of Baer and p.p.-rings. J. Aust. Math. Soc. 18, 470–473 (1974)

    Article  MathSciNet  Google Scholar 

  5. Boisen, M., Jr., Sheldon, P.: CPI-extension: overrings of integral domains with special prime spectrum. Canad. J. Math. 29, 722–737 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  6. D’Anna, M.: A construction of Gorenstein rings. J. Algebra 306(2), 507–519 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. D’Anna, M., Finacchiaro, C.A., Fontana, M.: Amalgamated algebras along an ideal. Comm. Algebra Appl. pp. 241–252. (2009)

  8. D’Anna, M., Fontana, M.: An amalgamated duplication of a ring along an ideal: the basic properties. J. Algebra Appl. 6(3), 443–459 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dorroh, J.L.: Concerning adjunctions to algebras. Bull. Amer. Math. Soc. 38, 85–88 (1932)

    Article  MathSciNet  MATH  Google Scholar 

  10. Finocciaro, C., Fontana, M.: Prüfer-like conditions on an amalgamated algebra along an ideal. Houston J. Math. 40(1), 63–79 (2014)

    MathSciNet  Google Scholar 

  11. Huh, C., Lee, Y., Smoktunowicz, A.: Armendariz and semicommutative rings. Comm. Algebra 30(2), 751–761 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kabbaj, S., Louartiti, K., Tamekkante, M.: Bi-amalgamated algebras along ideals. J. Commut. Algebra 65–87 (2017)

  13. Kim, N.K., Lee, Y.: Armendariz rings and reduced rings. J. Algebra 223, 477–488 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lee, T.K., Wong, T.L.: On Armendariz rings. Houston J. Math 29, 583–593 (2003)

    MathSciNet  MATH  Google Scholar 

  15. Liu, Z., Zhao, R.: On weak Armendariz rings. Comm. Algebra 34, 2607–2616 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mahdou, N., Mimouni, A., El Ourrachi, M.: On Armendariz like properties in amalgamated algebras along ideals. Turk. J. Math. 41, 1673–1686 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. Nagata, M.: Local Rings. Interscience, New York (1962)

    MATH  Google Scholar 

  18. Reg, M., Chhawchharia, S.: Armendariz rings. Proc. Japan Acad. Ser. A Math. Sci. 73, 14–17 (1997)

    MathSciNet  MATH  Google Scholar 

  19. Shin, G.: Prime ideals and sheaf representation of a pseudo symmetric rings. Trans. Am. Soc. 184, 43–60 (1973)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Economics and Social Sciences of Fez, University S.M. Ben Abdellah, Fez, Morocco

    Mohamed Chhiti

  2. Department of Mathematics, Faculty of Science and Technology of Fez, University S.M. Ben Abdellah, P.O. Box 2202, Fez, Morocco

    Loubna Es-Salhi

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  1. Mohamed Chhiti
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  2. Loubna Es-Salhi
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Correspondence to Mohamed Chhiti.

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Chhiti, M., Es-Salhi, L. Armendariz-like properties in bi-amalgamations. Bol. Soc. Mat. Mex. 28, 69 (2022). https://doi.org/10.1007/s40590-022-00459-y

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  • DOI: https://doi.org/10.1007/s40590-022-00459-y

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