International Journal of Theoretical and Applied Mathematics

Volume 6, Issue 1, February 2020

  • Associated Primes of Powers of Monomial Ideals: A Survey

    Mehrdad Nasernejad

    Issue: Volume 6, Issue 1, February 2020
    Pages: 1-13
    Received: 21 October 2019
    Accepted: 12 November 2019
    Published: 30 December 2019
    Abstract: Let R be a commutative Noetherian ring and I be an ideal of R. We say that I satisfies the persistence property if AssR(R/Ik) ⊆ AssR(R/Ik+1) for all positive integers k, where AssR(R/I ) denotes the set of associated prime ideals of I. In addition, an ideal I has the strong persistence property if (Ik+1: RI) = Ik for all positive integers k. Also, ... Show More
  • Volume Integral Mean of Holomorphic Function on Polydisc

    Lijuan Xu, Hua Liu, Juan Chen, Xiaoli Bian

    Issue: Volume 6, Issue 1, February 2020
    Pages: 14-18
    Received: 17 December 2019
    Accepted: 4 January 2020
    Published: 13 January 2020
    Abstract: Let f be an analytic function in the Hardy space on the polydisc P2. In this article we discuss the area integral means Mp (f, r) of f on the polydisc P2 with radius r, and its weighted volume means Mp,α (f, r) with to the weight (1-|z1|2)a×(1-|z2|2)a. We prove that both Mp (f, r) and Mp,α (f, r) are strictly increasing in r unless f is a constant.... Show More