Skew lattices in rings

DOI10.1007/BF01243872zbMath0669.06006MaRDI QIDQ1118623

Jonathan Leech

Publication date: 1989

Published in: Algebra Universalis (Search for Journal in Brave)

zbMATH Keywords

Artinian ringscongruence relationrectangular skew latticemaximal rectangular subalgebrasnoncommutative latticeskew lattices in rings

Mathematics Subject Classification ID

Lattices (06B99)

Related Items (47)

Flat coset decompositions of skew lattices ⋮ Skew Boolean algebras and discriminator varieties ⋮ Distributivity in skew lattices ⋮ Skew Boolean algebras ⋮ Recent developments in the theory of skew lattices ⋮ Categorical skew lattices ⋮ A non-commutative Priestley duality. ⋮ Boolean product representations of algebras via binary polynomials ⋮ On the coset laws for skew lattices ⋮ Residuated skew lattices ⋮ Stone duality for spectral sheaves and the patch monad ⋮ Dual skew Heyting almost distributive lattices ⋮ Homology of distributive lattices ⋮ Cancellation in skew lattices ⋮ Factor varieties ⋮ On pseudo residuated skew lattices ⋮ Filters theory on pseudo residuated skew lattices ⋮ A refinement of Stone duality to skew Boolean algebras ⋮ Noncommutative frames ⋮ On strongly symmetric skew lattices ⋮ Duality for noncommutative frames ⋮ Skew lattices and binary operations on functions ⋮ Normal skew lattices ⋮ A DUALIZING OBJECT APPROACH TO NONCOMMUTATIVE STONE DUALITY ⋮ MACE4 and SEM: A Comparison of Finite Model Generators ⋮ Associativity of the \(\nabla\)-operation on bands in rings. ⋮ Coset laws for categorical skew lattices ⋮ Ultrafilter extensions of linearly ordered sets. ⋮ Unnamed Item ⋮ My journey into noncommutative lattices and their theory ⋮ On the structure of semigroups of idempotent matrices. ⋮ The Geometric Structure of Skew Lattices ⋮ Groupoids on a skew lattice of objects ⋮ Ω-lattices from skew lattices ⋮ On the coset structure of distributive skew lattices ⋮ On noncommutative generalisations of Boolean algebras ⋮ Dual binary discriminator varieties ⋮ On the coset category of a skew lattice. ⋮ Noncommutative frames revisited ⋮ ON MAXIMAL IDEMPOTENT-CLOSED SUBRINGS OF M_n(𝔽) ⋮ On the coset structure of a skew lattice ⋮ Skew lattices and set-theoretic solutions of the Yang-Baxter equation ⋮ Unnamed Item ⋮ Internal Decompositions of Skew Lattices ⋮ The connection of skew Boolean algebras and discriminator varieties to Church algebras ⋮ Rings Whose Idempotents Form a Multiplicative Set ⋮ Unnamed Item

Cites Work

• Normal skew lattices
• Zur Charakterisierung distributiver Schiefverbände
• Schrägverbände und Quasiordnungen
• Über nichtkommutative Verbände
• Pseudosemilattices and pseudolattices
• The Geometric Structure of Skew Lattices
• Halbgruppen von Idempotenten und nichtkommutative Verbände.
• Lattices With Unique Complements
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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