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Boletín de la Sociedad Matemática Mexicana

, Volume 25, Issue 3, pp 543–549 | Cite as

Detecting the maximal-associated prime ideal of monomial ideals

  • Mehrdad Nasernejad
  • Saeed RajaeeEmail author
Original Article

Abstract

Let I be a monomial ideal in a polynomial ring \(R=K[x_1, \ldots , x_n]\) and \({\mathfrak {m}}=(x_1, \ldots , x_n)\) be the graded maximal ideal of R. In this paper, we provide a necessary and sufficient condition whether \({\mathfrak {m}}\in \mathrm {Ass}_R(R/I)\), where \(\mathrm {Ass}_R(R/I)\) denotes the set of associated prime ideals of I.

Keywords

Associated primes Monomial ideals 

Mathematics Subject Classification

13B25 13F20 

Notes

Acknowledgements

The authors are deeply grateful to the referee for careful reading of the manuscript and helpful comments and for her/his valuable suggestions which led to some improvements in the quality of this paper.

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Copyright information

© Sociedad Matemática Mexicana 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of MathematicsPayame Noor University (PNU)TehranIran
  2. 2.Department of MathematicsKhayyam UniversityMashhadIran

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