dL-Filters of principal MS-algebras

Badawy, Abd El-Mohsen

doi:10.1016/j.joems.2014.12.008

Cited by 10 publications

(5 citation statements)

References 3 publications

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“…We get that E T (E T (Z)) = E T (T ) = L. Thus (2) implies (1). Consider (1). Therefore E T (E T (Z)) = L. By Lemma 3.1 (6), L ∩ E T (Z) = T .…”

Section: Extended Filtermentioning

confidence: 97%

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Extended Filters of MS -Algebras

Gaber,

Seoud,

Tarek

2023

MJMS

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For a filter T of an MS -algebra L and a subset Z of L, a new extension filter of T is introduced, denoted by ET(Z). Many properties of ET(Z) are investigated and the lattice structure of the set of all ET(Z) is studied. A new definition related to ET(Z) is presented, called fixed filters relative to a subset of L. A generalisation of ET(Z) is illustrated by introducing the concept of strong filters, notated by ET(Z)¯¯¯¯¯¯¯¯¯¯¯¯¯¯. The strong extension ET(Z)¯¯¯¯¯¯¯¯¯¯¯¯¯¯ is characterized by the intersection of all strong filters fixed relative to an ideal L−P for a prime filter P of L.

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“…We get that E T (E T (Z)) = E T (T ) = L. Thus (2) implies (1). Consider (1). Therefore E T (E T (Z)) = L. By Lemma 3.1 (6), L ∩ E T (Z) = T .…”

Section: Extended Filtermentioning

confidence: 97%

“…The class MS is a subclass of Berman class K 1,1 which introduced by Berman in [3]. The theory of filters such as d L -filters [1] and β-filters [12] of MS-algebras has been studied by many authors. In the twenty-first century, many related structures to lattice theory and MS-algebras [10,11] had a great concern.…”

Section: Introductionmentioning

confidence: 99%

Extended Filters of MS -Algebras

Gaber,

Seoud,

Tarek

2023

MJMS

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“…Also, A. Badawy [2] gave a construction of DMS c -algebras generalizing the construction due to T. Katriňāk [11] for regular double Stone algebras. Many important properties of MS-algebras and double MS-algebras deal with homomorphisms, subalgebras, filters and congruences are studied in [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Constraction of a core regular double MS-algebra

El-Mohsen¹

2020

Filomat

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In this paper, we introduce and characterize a core regular double MS-algebra. A construction of a core regular double MS-algebra M [2] via a de Morgan algebra M is given. A one to one correspondence between the class of de Morgan algebras and the class of core regular double MS-algebras is obtained. According to such construction we investigate many properties of a core regular double MS-algebra deal with subalgebras, homomorphisms, atoms and dual atoms. A description of an atomic core regular double MS-algebra is established. Also, we discuss some properties of a complete core regular double MS-algebra.

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“…Also, they formulated and solved some fill in problems concerning homomorphisms and subalgebras of decomposable MS-algebras. A. Badawy [5] introduced the notion of d L -filters of principal MS-algebras. Recently, A. Badawy [6] studied the relationship between de Morgan filters and congruences of decomposable MS-algebras.…”

Section: Introductionmentioning

confidence: 99%

Complete decomposable MS-algebras

Badawy

Gaber

2019

J Egypt Math Soc

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According to the characterization of decomposable MS-algebras in terms of triples (M, D, ϕ), where M is a de Morgan algebra, D is a distributive lattice with 1 and ϕ is a (0,1)-homomorphism of M into F(D), the filter lattice of D, we characterize complete decomposable MS-algebras in terms of complete decomposable MS-triples. Also, we describe the complete homomorphisms of complete decomposable MS-algebras by means of complete decomposable MS-triples.

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dL-Filters of principal MS-algebras

Cited by 10 publications

References 3 publications

Extended Filters of MS -Algebras

Extended Filters of MS -Algebras

Constraction of a core regular double MS-algebra

Complete decomposable MS-algebras

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