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<p>The purpose of this paper is to investigate a new equational class of algebras called semi-De Morgan almost distributive lattices as a non-commutative generalization of semi-De Morgan algebras. It is observed that the class of semi-De Morgan almost distributive lattices is the smallest variety of algebras properly containing each of the class of semi-De Morgan algebras, the class of pseudo-complemented almost distributive lattices and the class of De Morgan almost distributive lattices. We further investigate some special classes of semi-De Morgan almost distributive lattices called demi <i>p</i>-almost distributive lattices (respectively, near <i>p</i>-almost distributive lattices) and give their characterizations in terms of Stone almost distributive lattices as well as pseudo-complemented almost distributive lattices. It is also proved that the class of demi <i>p</i>-almost distributive lattices satisfies the congruence extension property.</p>

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Semi-De Morgan almost distributive lattices

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Gezahagne Mulat Addis,
  • Wondwosen Zemene Norahun,
  • B. Davvaz

摘要

The purpose of this paper is to investigate a new equational class of algebras called semi-De Morgan almost distributive lattices as a non-commutative generalization of semi-De Morgan algebras. It is observed that the class of semi-De Morgan almost distributive lattices is the smallest variety of algebras properly containing each of the class of semi-De Morgan algebras, the class of pseudo-complemented almost distributive lattices and the class of De Morgan almost distributive lattices. We further investigate some special classes of semi-De Morgan almost distributive lattices called demi p-almost distributive lattices (respectively, near p-almost distributive lattices) and give their characterizations in terms of Stone almost distributive lattices as well as pseudo-complemented almost distributive lattices. It is also proved that the class of demi p-almost distributive lattices satisfies the congruence extension property.