On derivations of lattices

Xin, Xiao Long; Li, Ti Yao; Lü, Jing

doi:10.1016/j.ins.2007.08.018

Cited by 61 publications

(49 citation statements)

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“…There are many articles that talk about generalized derivations on rings and rings close (for example see the following references [5] and [6]). Also many papers have talked about derivations, generalized derivations over lattices as [1], [2], [8], [10], [11], [12].…”

Section: Introductionmentioning

confidence: 99%

On generalized derivations of partially ordered sets

Abdelwanis

Boua

2019

Communications in Mathematics

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Let P be a poset and d be a derivation on P . In this research, the notion of generalized d-derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized d-derivations are introduced. The properties of the fixed points based on the generalized d-derivations are examined. The properties of ideals and operations related with generalized d-derivations are studied.2010 MSC: 06E20, 13N15, 06Axx.

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Section: Introductionmentioning

confidence: 99%

On generalized derivations of partially ordered sets

Abdelwanis

Boua

2019

Communications in Mathematics

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“…There are many authors who studied derivations in various algebraic structures, such as rings, lattices, BCI-algebra and subtraction algebras, etc [11][12][13][14][15]. In [16], we introduced the notion of derivation for a quantale, and we discussed some related properties.…”

Section: Introductionmentioning

confidence: 99%

On derivations of quantales

Xiao

Liu

2016

Open Mathematics

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A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It's well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.

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“…Recently the properties of lattices were widely researched ( [1], [2], [5], [10], [12], [20], [22]). In the theory of rings and near rings, the properties of derivations are an important topic to study ([3], [4], [19]).…”

Section: Introductionmentioning

confidence: 99%