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Distributive implication groupoids

100%

Chajda I., Halaš R.

Open Mathematics

2007

tom 5

nr 3

484-492

We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.

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On varieties of left distributive left idempotent groupoids

86%

Stanovský D.

Discussiones Mathematicae - General Algebra and Applications

2004

tom 24

nr 2

267-275

We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity xⁿ ≈ x decomposes as the direct product of its largest idempotent factor and a cycle. Some properties of subdirectly ireducible LDLI groupoids are found.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Open Mathematics

1 Chajda I.

1 Halaš R.

1 Stanovský D.

1 2007

1 2004

Wyniki wyszukiwania

Distributive implication groupoids

On varieties of left distributive left idempotent groupoids