Geodesic
On Sheffer Stroke BE-Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 293-314.

Voir la notice de l'article provenant de la source Library of Science

In this paper we introduce Sheffer stroke BE-algebras (briefly, SBE-algebras) and investigate a relationship between SBE-algebras and BE-algebras. By presenting a SBE-filter, an upper set and a SBE-subalgebra on a SBE-algebra, it is shown that any SBE-filter of a SBE-algebra is a SBE-subalgebra but the converse of this statement is not true. Besides we construct quotient SBE-algebras via a congruence relation defined by a special SBE-filter. We discuss SBE-homomorphisms and their properties between SBE-algebras. Finally, a relation between Sheffer stroke Hilbert algebras and SBE-algebras is established.
Keywords: Sheffer stroke, SBE-algebra, congruence, SBE-homomorphism 
@article{DMGAA_2022_42_2_a3,
     author = {Katican, Tugce and Oner, Tahsin and Saeid, Arsham Borumand},
     title = {On {Sheffer} {Stroke} {BE-Algebras}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {293--314},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a3/}
}
TY  - JOUR
AU  - Katican, Tugce
AU  - Oner, Tahsin
AU  - Saeid, Arsham Borumand
TI  - On Sheffer Stroke BE-Algebras
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2022
SP  - 293
EP  - 314
VL  - 42
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a3/
LA  - en
ID  - DMGAA_2022_42_2_a3
ER  - 
%0 Journal Article
%A Katican, Tugce
%A Oner, Tahsin
%A Saeid, Arsham Borumand
%T On Sheffer Stroke BE-Algebras
%J Discussiones Mathematicae. General Algebra and Applications
%D 2022
%P 293-314
%V 42
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a3/
%G en
%F DMGAA_2022_42_2_a3
Katican, Tugce; Oner, Tahsin; Saeid, Arsham Borumand. On Sheffer Stroke BE-Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 293-314. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a3/

[1] J.C. Abbott, Implicational algebras, Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie 11 ( 59 ) (1967) 3–23. https://www.jstor.org/stable/43679502

[2] S.S. Ahn and K.S. So, On Ideals and Upper Sets BE-algebra, Sci. Math. Japon. 68 (2) (2008) 29–285. https://doi.org/10.32219/ISMS.68.2 279

[3] S.S. Ahn and K.S. So, On Generalized upper sets BE-algebra, Bull. Korean Math. Soc. 46 (2) (2009) 281–287. https://doi.org/10.4134/BKMS.2009.46.2.281

[4] I. Chajda, Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 44 (2005) 19–23. https://dml.cz/handle/10338.dmlcz/133381

[5] I. Chajda, R. Halaš and H. Länger, Operations and structures derived from non-associative MV-algebras, Soft Computing 23 (12) (2019) 3935–3944. https://doi.org/10.1007/s00500-018-3309-4

[6] H.S. Kim and Y.H. Kim, On BE-algebras, Sci. Math. Jpn. online e-2006 (2006) 1299–1302.

[7] W. McCune, R. Veroff, B. Fitelson, K. Harris, A. Feist and L. Wos, Short single axioms for Boolean algebra, J. Automated Reasoning 29 (2002) 1–16. https://doi.org/10.1023/A:1020542009983

[8] T. Oner, T. Katican and A. Borumand Saeid, Relation between Sheffer stroke operation and Hilbert algebras, Categories and General Algebraic Structures with Applications 14 (2021) 245–268. https://doi.org/10.29252/cgasa.14.1.245

[9] T. Oner, T. Katican and A. Borumand Saeid, (Fuzzy) filters of Sheffer stroke BL-algebras, Kragujevac J. Math. 47 (2023) 39–55.

[10] T. Oner, T. Katican, A. Borumand Saeid and M. Terziler, Filters of strong Sheffer stroke non-associative MV-algebras, Analele Stiintifice ale Universitatii Ovidius Constanta 29 (2021) 143–164. https://doi.org/10.2478/auom-2021-0010

[11] T. Oner, T. Katican and A. Borumand Saeid, Fuzzy filters of Sheffer stroke Hilbert algebras, J. Intelligent and Fuzzy Syst. 40 (2021) 759–772. https://doi.org/10.3233/JIFS-200760

[12] T. Oner, T. Katican and A. Borumand Saeid, On Sheffer stroke UP-algebras, Discuss. Math. Gen. Alg. and Appl. 41 (2021) 381–394.

[13] A. Rezaei, A. Borumand Saeid and R.A. Borzooei, Relation between Hilbert Algebras and BE-algebras, Application and Applied Mathematics: An International Journal 8 (2013) 573–584. https://doi.org/10.7151/dmgaa.1285

[14] A. Rezaei and A. Borumand Saeid, Some Results in BE-algebras, Analele Universităţii Oradea Fasc. Matematica XIX (1) (2012) 33–44.

[15] A. Rezaei and A. Borumand Saeid, Relation between BE-algebras and g-Hilbert algebras, Discuss. Math. Gen. Alg. and Appl. 38 (2018) 33–45. https://doi.org/10.7151/dmgaa.1285

[16] A. Rezaei and A. Borumand Saeid, Relation between dual S-algebras and BE-algebras, Le Mathematiche LXX (I) (2015) 71–79. https://doi.org/10.4418/2015.70.1.5

[17] A. Rezaei and A. Borumand Saeid, Commutative Ideals in BE-algebras, Kyungpook Math. J. 52 (52) (2012) 483–494. https://doi.org/10.5666/KMJ.2012.52.4.483

[18] H. P. Sankappanavar and S. Burris, A course in universal algebra, Graduate Texts Math. 78 (1981).

[19] H. M. Sheffer, A set of five independent postulates for Boolean algebras, with application to logical constants, Trans. Amer. Math. Soc. 14 (1913) 481-488. https://doi.org/10.2307/1988701

[20] A. Walendziak, On Commutative BE-algebras, Sci. Math. Japon. 69 (2008) 585–588.

[21] A. Najafi and A. Borumand Saeid, Fuzzy points in BE-algebras, J. Mahani Math. Res. Center 8 (1.2) (2019) 69–80. https://doi.org/10.22103/JMMRC.2019.12457.1065