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2 results

  • GROWTH RATES OF ALGEBRAS, I: POINTED CUBE TERMS

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  • KEITH A. KEARNES, EMIL W. KISS, ÁGNES SZENDREI
  • Journal:
    Journal of the Australian Mathematical Society / Volume 101 / Issue 1 / August 2016
    Published online by Cambridge University Press:
    22 January 2016, pp. 56-94
    Print publication:
    August 2016
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  • We investigate the function $d_{\mathbf{A}}(n)$, which gives the size of a least size generating set for $\mathbf{A}^{n}$.

  • Simple surjective algebras having no proper subalgebras

  • Part of
  • Ágnes Szendrei
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 48 / Issue 3 / June 1990
    Published online by Cambridge University Press:
    09 April 2009, pp. 434-454
    Print publication:
    June 1990
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  • We prove that every finite, simple, surjective algebra having no proper subalgebras is either quasiprimal or affine or isomorphic to an algebra term equivalent to a matrix power of a unary permutational algebra. Consequently, it generates a minimal variety if and only if it is quasiprimal. We show also that a locally finite, minimal variety omitting type 1 is minimal as a quasivariety if and only if it has a unique subdirectly irreducible algebra.