Congruence pairs of principal p-algebras
-
Abd El-Mohsen Badawy
Abstract
In this paper, we first introduce the concept of congruence pairs on the class of principal p-algebras. Then, we show that every congruence relation θ on a principal p-algebra L can be uniquely determined by a congruence pair (θ1, θ2). Moreover, the strong extensions of principal p-algebras and the permutability of congruences will be investigated by congruence pairs.
Acknowledgement
The authors would like to thank the referee for his useful comments and valuable suggestions given to this paper.
References
[1] Badawy, A.—Shum, K. P.: Congruences and Boolean filters of quasi-modular p-algebras, Discuss. Math. Gen. Algebra Appl. 34 (2014), 109–123.10.7151/dmgaa.1212Search in Google Scholar
[2] Badawy, A.—Atallah, M.: Boolean filters of principal p-algebras, Int. J. Math. Comput. 26 (2015), 15–25.Search in Google Scholar
[3] Badawy, A.: Filters of p-algebras with respect to a closure operator, Southeast Asian Bull. Math. 40 (2016), 34–47.Search in Google Scholar
[4] Berman, J.: Congruence relations of pseudocomplemented distributive lattices, Algebra Univ. 3 (1973), 388–293.10.1007/BF02945130Search in Google Scholar
[5] Berman, J.: Notes on Equational Classes of Algebras. Lecture Notes, Univ. of Chicago, 1974.Search in Google Scholar
[6] Birkhof, G.: Lattice Theory, Colloquium Publications 25, Amer. Math. Soc., New York, 1967.Search in Google Scholar
[7] El-Assar, S.—Abdel-Hakim, M.: Two notes of modular p-algebras, Qatar Univ. Sci. Bull. 81 (1988), 23–28.Search in Google Scholar
[8] El-Assar, S.: Strong extension of quasi-modular p-algebras, Delta J. Sci. 12 (1998), 843–851.Search in Google Scholar
[9] Lakser, H.: The structure of pseudocomplemented distributive lattices. I: Subdirect decomposition, Trans. Amer. Math. Soc. 156 (1971), 335–342.Search in Google Scholar
[10] Grätzer, G.: Lattice Theory: First Concepts and Distributive Lattices. Freeman, San Francisco, 1971.Search in Google Scholar
[11] Haviar, M.: Construction and affine completeness of principal p-algebras, Tatra Mt. Math. Publ. 5 (1995), 217–228.Search in Google Scholar
[12] Katriňák, T.: Über eine konstruktion der distributiven pseudokomplementren verbände, Math. Nachr. 53 (1972), 85–99.10.1002/mana.19720530109Search in Google Scholar
[13] Katriňák, T.: p-algebras. In: Contributions to Lattice Theory, Szeged, 1980 Colloq. Math. Soc. Janos Bolyai 33 (1983), 549–573.Search in Google Scholar
[14] Katriňák, T.: Essential and strong extensions of p-algebras, Bull. Soc. Roy. Sci. Liège 3-4 (1980), 119–124.Search in Google Scholar
[15] Katriňák, T.—Mederly, P.: Construction of p-algebras, Algebra Universalis 4 (1983), 288–316.10.1007/BF01194538Search in Google Scholar
[16] Katriňák, T.: Free distributive p-algebras, a new approach, Glasg. Math. J. 40 (1988), 333–342.10.1017/S0017089500032687Search in Google Scholar
[17] Ribenboim, P.: Characterization of the sup-complement in a distributive latttice with last element, Summa Brasil. Math. 2 (1949), 43–49.Search in Google Scholar
[18] Varlet, J. C.: A strengthening of the notion of essential extension. Bull. Soc. Roy. Sci. Liège 11-12, (1979), 432–437.Search in Google Scholar
[19] Sambasiva Rao, M.—Badawy, A.: μ-filters of distributive lattices, Southeast Asian Bull. Math. 40 (2016), 251–264.Search in Google Scholar
[20] Sambasiva Rao, M.—Badawy, A.: Filters of lattices with respect to a congruence, Discuss. Math. Gen. Algebra Appl. 34 (2014), 213–219.Search in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- State hoops
- On derivations of partially ordered sets
- Interior and closure operators on commutative basic algebras
- When is the cayley graph of a semigroup isomorphic to the cayley graph of a group
- Sequences of cantor type and their expressibility
- δ-Fibonacci and δ-lucas numbers, δ-fibonacci and δ-lucas polynomials
- Law of inertia for the factorization of cubic polynomials – the case of primes 2 and 3
- Closed hereditary coreflective subcategories in epireflective subcategories of Top
- Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments
- Difference of two strong Światkowski lower semicontinuous functions
- Fejér-type inequalities (II)
- Representation of maxitive measures: An overview
- On a conjecture of Y. H. Cao and X. B. Zhang
- On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces
- Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups
- Homological properties of banach modules over abstract segal algebras
- Variable Hajłasz-Sobolev spaces on compact metric spaces
- Commuting pairs of self-adjoint elements in C*-algebras
- Additivity of maps preserving products AP ± PA* on C*-algebras
- A note on derived connections from semi-symmetric metric connections
- Lindelöf P-spaces need not be Sokolov
- Strong convergence properties for arrays of rowwise negatively orthant dependent random variables
- Least absolute deviations problem for the Michaelis-Menten function
- Congruence pairs of principal p-algebras
Articles in the same Issue
- State hoops
- On derivations of partially ordered sets
- Interior and closure operators on commutative basic algebras
- When is the cayley graph of a semigroup isomorphic to the cayley graph of a group
- Sequences of cantor type and their expressibility
- δ-Fibonacci and δ-lucas numbers, δ-fibonacci and δ-lucas polynomials
- Law of inertia for the factorization of cubic polynomials – the case of primes 2 and 3
- Closed hereditary coreflective subcategories in epireflective subcategories of Top
- Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments
- Difference of two strong Światkowski lower semicontinuous functions
- Fejér-type inequalities (II)
- Representation of maxitive measures: An overview
- On a conjecture of Y. H. Cao and X. B. Zhang
- On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces
- Almost everywhere convergence of some subsequences of Fejér means for integrable functions on some unbounded Vilenkin groups
- Homological properties of banach modules over abstract segal algebras
- Variable Hajłasz-Sobolev spaces on compact metric spaces
- Commuting pairs of self-adjoint elements in C*-algebras
- Additivity of maps preserving products AP ± PA* on C*-algebras
- A note on derived connections from semi-symmetric metric connections
- Lindelöf P-spaces need not be Sokolov
- Strong convergence properties for arrays of rowwise negatively orthant dependent random variables
- Least absolute deviations problem for the Michaelis-Menten function
- Congruence pairs of principal p-algebras
