Quadruple construction of decomposable double MS-algebras
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Abd El-Mohsen Badawy
,
Salah El-Din S. Hussein
Abstract
This paper is devoted to the study of the class of decomposable double MS-algebras. Necessary and sufficient conditions for a decomposable MS-algebra to be a decomposable double MS-algebra are deduced. We construct decomposable double MS-algebras by means of decomposable MS-quadruples and we prove that there exists a one-to-one correspondence between decomposable double MS-algebras and decomposable MS-quadruples. Moreover, a construction of decomposable K2-algebras (Stone algebras) by means of K2-quadruples (Stone quadruples) is given. We conclude by introducing and characterizing isomorphisms of decomposable double MS-algebras in terms of decomposable MS-quadruples.
Acknowledgement
We thank the editor and the referee for their valuable comments and suggestions for improving the paper.
(Communicated by Jan Kühr)
References
[1] Badawy, A.—Guffova D.—Haviar, M.: Triple construction of decomposable MS-algebras, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 51(2) (2012), 53–65.Suche in Google Scholar
[2] Badawy, A.—El-Fawal, R.: Homomorphisms and subalgebras of decomposable MS-algebra, J. Egyptian Math. Soc. 25(2) (2017), 119–124.10.1016/j.joems.2016.10.001Suche in Google Scholar
[3] Badawy, A.—Atallah, M.: MS-intervals of an MS-algebra, Hacet. J. Math. Stat. 48(5) (2019), 1479–1487.10.15672/HJMS.2018.590Suche in Google Scholar
[4] Badawy, A.: Balanced factor congruences of double MS-algebras, J. Egyptian Math. Soc. 27(6) (2019), 1–15.10.1186/s42787-019-0008-ySuche in Google Scholar
[5] Badawy, A.: dL-Filters of principal MS-algebras, J. Egyptian Math. Soc. 23 (2015), 463–469.10.1016/j.joems.2014.12.008Suche in Google Scholar
[6] Badawy, A.: Regular double MS-algebras, Appl. Math. Inf. Sci. 11(2) (2017), 115–122.10.18576/amis/110114Suche in Google Scholar
[7] Badawy, A.: Extensions of the Glivenko-type congruences on a Stone lattice, Math. Methods Appl. Sci. 41(15) (2018), 5719–5732.10.1002/mma.4492Suche in Google Scholar
[8] Badawy, A.: Construction of core regular double MS-algebras, Filomat 34(1) (2018), 35–50.10.2298/FIL2001035BSuche in Google Scholar
[9] Badawy, A.—Gaber, A.: Complete decomposable MS-algebras, Egyptian Math. Soc. 72 (2019), Art. ID 23.10.1186/s42787-019-0027-8Suche in Google Scholar
[10] Badawy, A.—El-Fawal, R.: Closure filters of decomposable MS-algebras, Southeast Asian Bull. Math. 44 (2020), 177–194.Suche in Google Scholar
[11] Badawy, A.: Congruences and De Morgan filters of decomposable MS-algebras, Southeast Asian Bull. Math. 43 (2019), 13–25.Suche in Google Scholar
[12] Badawy, A.—Sambasiva Rao, M.: Clouser ideals of MS-algebras, Chamchuri J. Math. 6 (2014), 31–46.Suche in Google Scholar
[13] Gaber, A.—Badawy, A.—Hussein, S.: On decomposable MS-algebras, Ital. J. Pure Appl. Math. 43 (2020), 617–626.Suche in Google Scholar
[14] Blyth, T. S.—Varlet, J. C.: Sur la construction de certaines MS-algebres, Port. Math. 39 (1980), 489–496.Suche in Google Scholar
[15] Blyth, T. S.—Varlet, J. C.: Corrigendum sur la construction de certaines MS-algebres, Port. Math. 42 (1983), 469–471.Suche in Google Scholar
[16] Blyth, T. S.—Varlet, J. C.: On a common abstraction of de Morgan algebras and Stone algebras, Proc. Roy. Soc. Edinburgh 94A (1983), 301–308.10.1017/S0308210500015663Suche in Google Scholar
[17] Blyth, T. S.—Varlet, J. C.: Subvarieties of the class of MS-algebras, Proc. Roy. Soc. Edinburgh 95A (1983), 157–169.10.1017/S0308210500015869Suche in Google Scholar
[18] Blyth, T. S.—Varlet, J. C.: Ockham Algebras, University Press, London, Oxford 1994.10.1093/oso/9780198599388.001.0001Suche in Google Scholar
[19] Blyth, T. S.—Varlet, J. C.: Double MS-algebras, Proc. Roy. Soc. Edinburgh 94 (1984), 157–169.10.1017/S0308210500025543Suche in Google Scholar
[20] Congwen, L.: The class of double MS-algebras satisfying the complement property, Bulletin de la Société des Sciences de Liège, 70(1) (2001), 51–59.Suche in Google Scholar
[21] Haviar, M.: On certain construction of MS-algebras. Port. Math. 51 (1994), 71–83.Suche in Google Scholar
[22] Haviar, M.: Construction and affine completeness of principal p-algebras, Tatra Mt. Math. Publ. 5 (1995), 217–228.Suche in Google Scholar
[23] Haviar, M.: Affine complete algebras abstracting double Stone and Kleene algebras, Acta Univ. M. Belii Ser. Math. 4 (1996), 39–52.Suche in Google Scholar
[24] Katriňák, T.: A new proof of the construction theorem for Stone agebras, Proc. Amer. Math. Soc. 40 (1973), 75–78.10.1090/S0002-9939-1973-0316335-0Suche in Google Scholar
[25] Katriňák, T.: Construction of modular double S-algebras, Algebra Universalis 8 (1978), 15–22.10.1007/BF02485365Suche in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Monadic pseudo BE-algebras
- Quadruple construction of decomposable double MS-algebras
- Fibonacci numbers in generalized Pell sequences
- Solutions of a generalized markoff equation in Fibonacci numbers
- Root separation for polynomials with reducible derivative
- Quadratic refinements of Young type inequalities
- Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
- Integration with respect to deficient topological measures on locally compact spaces
- Differential subordinations and Pythagorean means
- Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables
- Unbounded oscillation of fourth order functional differential equations
- Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term
- Entropy as an integral operator: Erratum and modification
- Unital topology on a unital l-group
- On the topological complexity of Grassmann manifolds
- Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
- Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses
- Two semigroup rings associated to a finite set of meromorphic functions
Artikel in diesem Heft
- Regular papers
- Monadic pseudo BE-algebras
- Quadruple construction of decomposable double MS-algebras
- Fibonacci numbers in generalized Pell sequences
- Solutions of a generalized markoff equation in Fibonacci numbers
- Root separation for polynomials with reducible derivative
- Quadratic refinements of Young type inequalities
- Sharp bounds for the Toader mean of order 3 in terms of arithmetic, quadratic and contraharmonic means
- Integration with respect to deficient topological measures on locally compact spaces
- Differential subordinations and Pythagorean means
- Analogs of Hayman’s Theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables
- Unbounded oscillation of fourth order functional differential equations
- Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term
- Entropy as an integral operator: Erratum and modification
- Unital topology on a unital l-group
- On the topological complexity of Grassmann manifolds
- Properties and methods of estimation for a bivariate exponentiated Fréchet distribution
- Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses
- Two semigroup rings associated to a finite set of meromorphic functions
