@article{ddf708c9-eebf-4674-b3fb-0f21760e1627,
  abstract     = {{<p>We investigate subalgebras of finite codimension in. In earlier work we have introduced a way of describing such subalgebras in terms of their so called (subalgebra) spectrum and a set of conditions for subalgebra membership that can be expressed by evaluating polynomials and their derivatives in points of the spectrum only. In this paper we focus on subalgebras with a single element in their spectrum. This includes, among others, all monomial subalgebras. Moreover, any subalgebra given by only conditions involving derivatives can be obtained as a finite intersection of algebras with single spectrum. Our main result is an efficient algorithm for finding the set of defining conditions given a set of generators for a single spectrum subalgebra. As an important step on the way to an algorithm we introduce a new canonical basis (with many similarities to SAGBI basis), that we name LAGBI basis, for our single spectrum algebras. We then find an efficient algorithm for computing a LAGBI basis and finally incorporate it into our main algorithm for finding defining conditions. In the process we also find the derivations of a single spectrum subalgebra.</p>}},
  author       = {{Kennerland, Erik and Torstensson, Anna and Ufnarovski, Victor}},
  issn         = {{0938-1279}},
  keywords     = {{Derivations; Polynomial subalgebra; SAGBI; Subalgebra spectrum}},
  language     = {{eng}},
  publisher    = {{Springer}},
  series       = {{Applicable Algebra in Engineering, Communications and Computing}},
  title        = {{Almost monomial subalgebras of and their LAGBI bases}},
  url          = {{http://dx.doi.org/10.1007/s00200-025-00712-7}},
  doi          = {{10.1007/s00200-025-00712-7}},
  year         = {{2026}},
}