On modular pairs in semilattices

Thakare, N. K.; Wasadikar, Meenakshi; Maeda, Shûichirô

doi:10.1007/bf01190435

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Iv) L(g2(l)) Is the Boolean Lattice Formed By All Subsets Of1

Remark1

Ii) If L Has the Property (A) (Resp (B)) And If To(s) Is St1

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Cited by 7 publications

(3 citation statements)

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“…(ii) follows from (iii), since the covering property is equivalent to (p, x)M* for p e I2(L) and x 6 L (see [6], Theorem 2.2). (i.e., a is a dual-atom) then only the element 1 covers a, and hence a is V-standard by (v).…”

Section: Iv) L(g2(l)) Is the Boolean Lattice Formed By All Subsets Ofmentioning

confidence: 95%

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On the ?del? relation in join-semilattices

Maeda

Thakare

Wasadikar

1985

Algebra Universalis

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Section: Iv) L(g2(l)) Is the Boolean Lattice Formed By All Subsets Ofmentioning

confidence: 95%

“…Let a, b be non-zero elements of an atomistic join-semilattice L. We write (a, b)P when p ~ I2(L), p -----a v b imply the existence of q, r e O(L) such that q --< a, r-----b and p ~ q v r (see [6], w THEOREM 3.5. Let L be an atomistic join-semilattice.…”

Section: Ii) If L Has the Property (A) (Resp (B)) And If To(s) Is Stmentioning

confidence: 99%

On the ?del? relation in join-semilattices

Maeda

Thakare

Wasadikar

1985

Algebra Universalis

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“…The question, How should one define a modular pair in a general poset?, was posed by Garret Birkhoff [1]. Birkhoff's problem was also investigated by Thakare-Maeda-Wasadikar [13] who discussed modular pairs for semilattices. Altogether there exist now five different concepts of modular pairs in a general poset (cf.…”

Section: Remarkmentioning

confidence: 99%

On forbidden configurations for strong posets

2004

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The concept of strong elements in posets is introduced. Several properties of strong elements in different types of posets are studied. Strong posets are characterized in terms of forbidden structures. It is shown that many of the classical results of lattice theory can be extended to posets. In particular, we give several characterizations of strongness for upper semimodular (USM) posets of finite length. We characterize modular pairs in USM posets of finite length and we investigate the interrelationships between consistence, strongness, and the property of being balanced in USM posets of finite length. In contrast to the situation in upper semimodular lattices, we show that these three concepts do not coincide in USM posets.

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Bibliography on quantum logics and related structures

Pavičić

1992

Int J Theor Phys

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On modular pairs in semilattices

Cited by 7 publications

References 4 publications

On the ?del? relation in join-semilattices

On the ?del? relation in join-semilattices

On forbidden configurations for strong posets

Bibliography on quantum logics and related structures

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