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Subalgebra analogue of Standard bases for ideals in $ K[[t_{1}, t_{2}, \ldots, t_{m}]][x_{1}, x_{2}, \ldots, x_{n}] $

  • Received: 18 August 2021 Revised: 01 November 2021 Accepted: 23 November 2021 Published: 22 December 2021
  • MSC : 13P10

  • In this paper, we develop a theory for Standard bases of $ K $-subalgebras in $ K[[t_{1}, t_{2}, \ldots, t_{m}]] [x_{1}, x_{2}, ..., x_{n}] $ over a field $ K $ with respect to a monomial ordering which is local on $ t $ variables and we call them Subalgebra Standard bases. We give an algorithm to compute subalgebra homogeneous normal form and an algorithm to compute weak subalgebra normal form which we use to develop an algorithm to construct Subalgebra Standard bases. Throughout this paper, we assume that subalgebras are finitely generated.

    Citation: Nazia Jabeen, Junaid Alam Khan. Subalgebra analogue of Standard bases for ideals in $ K[[t_{1}, t_{2}, \ldots, t_{m}]][x_{1}, x_{2}, \ldots, x_{n}] $[J]. AIMS Mathematics, 2022, 7(3): 4485-4501. doi: 10.3934/math.2022250

    Related Papers:

  • In this paper, we develop a theory for Standard bases of $ K $-subalgebras in $ K[[t_{1}, t_{2}, \ldots, t_{m}]] [x_{1}, x_{2}, ..., x_{n}] $ over a field $ K $ with respect to a monomial ordering which is local on $ t $ variables and we call them Subalgebra Standard bases. We give an algorithm to compute subalgebra homogeneous normal form and an algorithm to compute weak subalgebra normal form which we use to develop an algorithm to construct Subalgebra Standard bases. Throughout this paper, we assume that subalgebras are finitely generated.



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