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<p>We extend the work of Galatos (<CitationRef CitationID="CR5">2004</CitationRef>) on nested sums, originally called generalised ordinal sums, of residuated lattices. We show that the nested sum of an odd quasi relation algebra (qRA) satisfying certain conditions and an arbitrary qRA is again a qRA. In a recent paper by Craig and Robinson (<CitationRef CitationID="CR3">2025</CitationRef>) the notion of representability for distributive quasi relation algebras (DqRAs) was developed. For certain pairs of representable DqRAs, we prove that their nested sum is again representable. An important consequence of this result is that finite Sugihara chains are finitely representable.</p>

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Representability for Distributive Quasi Relation Algebras via Nested Sums

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月11日

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  • Andrew Craig,
  • Wilmari Morton,
  • Claudette Robinson

摘要

We extend the work of Galatos (2004) on nested sums, originally called generalised ordinal sums, of residuated lattices. We show that the nested sum of an odd quasi relation algebra (qRA) satisfying certain conditions and an arbitrary qRA is again a qRA. In a recent paper by Craig and Robinson (2025) the notion of representability for distributive quasi relation algebras (DqRAs) was developed. For certain pairs of representable DqRAs, we prove that their nested sum is again representable. An important consequence of this result is that finite Sugihara chains are finitely representable.