Skew lattices and binary operations on functions

Cvetko-Vah, Karin; Leech, Jonathan; Spinks, Matthew

doi:10.1016/j.jal.2013.03.011

Cited by 14 publications

(26 citation statements)

References 25 publications

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“…Proof. The map x → x (rk) is bijective because (x (rk) ) (rk) = x by Lemma 4.8 (6) and (B4). The map is a homomorphism: t r (x, y, z) (rk) = L.4.8 (7) t r (x, y (rk) , z (rk) ) = t r ((x (rk) ) (rk) , y (rk) , z (rk) ) = q((x (rk) ) (rk) , y (rk) /r, z (rk) /r) = L.4.8 (4) q(x (rk) , y (rk) /k, z (rk) /k) = t k (x (rk) , y (rk) , z (rk) ).…”

Section: 2mentioning

confidence: 94%

On noncommutative generalisations of Boolean algebras

Bucciarelli

Salibra

2019

Art Discrete Appl. Math.

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Skew Boolean algebras (skew BA) and Boolean-like algebras (nBA) are onepointed and n-pointed noncommutative generalisation of Boolean algebras, respectively. We show that any nBA is a cluster of n isomorphic right-handed skew BAs, axiomatised here as the variety of skew star algebras. The variety of skew star algebras is shown to be term equivalent to the variety of nBAs. We use skew BAs in order to develop a general theory of multideals for nBAs. We also provide a representation theorem for right-handed skew BAs in terms of nBAs of n-partitions.Date: May 30, 2019.

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Section: 2mentioning

confidence: 94%

On noncommutative generalisations of Boolean algebras

Bucciarelli

Salibra

2019

Art Discrete Appl. Math.

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“…(2) For different reasons, the SBA version of Theorem 5.8 also holds: every sub-quasi-variety of an SBA is actually a subvariety of the SBA. For the righthanded case, see [17,Theorem 12]. The term-equivalent left-handed case thus also holds.…”

Section: The Lattice Of Subvarietiesmentioning

confidence: 98%

“…Cvetko-Vah and Leech [15,16] have studied rings whose idempotents are closed under multiplication, and thus form SBAs that often have intersections. Both of the present authors with Cvetko-Vah [17] have studied applications to theoretical computer science. Spinks and his former advisor, Bignall, have studied connections with other types of algebras.…”

Section: Introductionmentioning

confidence: 99%