Homomorphisms and subalgebras of decomposable MS -algebras

Badawy, Abd El-Mohsen; El-Fawal, Ragaa.

doi:10.1016/j.joems.2016.10.001

Cited by 8 publications

(8 citation statements)

References 4 publications

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“…Now, let (x, y) ∈ θ a . We have (x, y) ∈ θ a ⇒ x ∨ a = y ∨ a ⇒ x + ∧ a + = (x ∨ a) + = (y ∨ a) + = y + ∧ a + by Proposition 1 (5) ⇒ (x + ∧ a + ) ∨ a = (y + ∧ a + ) ∨ a by joining two sides with a ⇒ (x + ∨ a) ∧ (a + ∨ a) = (x + ∨ a) ∧ (a + ∨ a) by the distributivity of L ⇒ x + ∨ a = x + ∨ a as a + ∨ a = 1.…”

Section: Proposition 3 For Any Two Elements a And B Of A Double Ms-almentioning

confidence: 90%

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Balanced factor congruences of double MS-algebras

Badawy

2019

J Egypt Math Soc

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In this paper, we introduce the concepts of Stone elements, central elements and Birkhoof central elements of a double MS-algebra and study their related properties. We observe that the center C(L) of a double MS-algebra L is precisely the Birkhoof center BC(L) of L. A complete description of factor congruences on a double MS-algebra is given by means of the central elements. A characterization of balanced factor congruences of double MS-algebra is obtained. A one-to-one correspondence between the class of all balanced factor congruences of a double MS-algebra L and the central elements of L is obtained.

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Section: Proposition 3 For Any Two Elements a And B Of A Double Ms-almentioning

confidence: 90%

“…Badawy [4] introduced and studied many properties of d L -filters of principal MSalgebras. Also, Badawy and El-Fawal [5] considered homomorphisms and subalgebras of decomposable MS-algebras.…”

Section: Introductionmentioning

confidence: 99%

Balanced factor congruences of double MS-algebras

Badawy

2019

J Egypt Math Soc

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“…In this section, we present definitions and main results which are needed through this paper. We refer the reader to [1][2][3][4][12][13][14][15] for more details.…”

Section: Preliminariesmentioning

confidence: 99%

“…Then, we characterize complete homomorphisms of complete decomposable MS-algebras in terms of complete triple homomorphisms. For this purpose, we recall from [4], the notion of triple homomorphism of decomposable MS-triples and related properties which will be used in rest of the paper.…”

Section: Complete Homomorphisms Via Complete Triple Homomorphismsmentioning

confidence: 99%

“…Moreover, they constructed a one-to-one correspondence between decomposable MS-algebras and decomposable MS-triples. A. Badawy and R. El-Fawal [4] studied many properties of decomposable MS-algebras in terms of decomposable MS-triples as homomorphisms and subalgebras. Also, they formulated and solved some fill in problems concerning homomorphisms and subalgebras of decomposable MS-algebras.…”

Section: Introductionmentioning

confidence: 99%

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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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On subalgebras of MS-algebras

Badawy,

EL-Maghrabi,

Helmy

2024

Soft Comput

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In this paper, we introduce the concepts of subalgebras, principal subalgebras and $$d_{L}$$ d L -subalgebras of a principal MS-algebra and describe the lattices of such subalgebras. Also, we describe a subalgebra [S] that generated by a subset S of an MS-algebra (principal MS-algebra) L and study related properties. Finally, we determine and characterize the principal subalgebras of a principal MS-algebra via admissible pairs.

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Homomorphisms and subalgebras of decomposable MS -algebras

Cited by 8 publications

References 4 publications

Balanced factor congruences of double MS-algebras

Balanced factor congruences of double MS-algebras

Complete decomposable MS-algebras

On subalgebras of MS-algebras

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