Strong endomorphism kernel property for finite Brouwerian semilattices and relative Stone algebras
Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 13-25
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We show that all finite Brouwerian semilattices have strong endomorphism kernel property (SEKP), give a new proof that all finite relative Stone algebras have SEKP and also fully characterize dual generalized Boolean algebras which possess SEKP.
We show that all finite Brouwerian semilattices have strong endomorphism kernel property (SEKP), give a new proof that all finite relative Stone algebras have SEKP and also fully characterize dual generalized Boolean algebras which possess SEKP.
DOI : 10.21136/MB.2023.0050-22
Classification : 03G25, 06E99, 08A30, 08A35, 08B26
Keywords: (strong) endomorphism kernel property; congruence relation; Brouwerian semilattice; Brouwerian algebra; dual generalized Boolean algebra; direct sum; factorable congruences
@article{10_21136_MB_2023_0050_22,
     author = {Guri\v{c}an, Jaroslav and Ghumashyan, Heghine},
     title = {Strong endomorphism kernel property for finite {Brouwerian} semilattices and relative {Stone} algebras},
     journal = {Mathematica Bohemica},
     pages = {13--25},
     year = {2024},
     volume = {149},
     number = {1},
     doi = {10.21136/MB.2023.0050-22},
     mrnumber = {4715553},
     zbl = {07830540},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0050-22/}
}
TY  - JOUR
AU  - Guričan, Jaroslav
AU  - Ghumashyan, Heghine
TI  - Strong endomorphism kernel property for finite Brouwerian semilattices and relative Stone algebras
JO  - Mathematica Bohemica
PY  - 2024
SP  - 13
EP  - 25
VL  - 149
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0050-22/
DO  - 10.21136/MB.2023.0050-22
LA  - en
ID  - 10_21136_MB_2023_0050_22
ER  - 
%0 Journal Article
%A Guričan, Jaroslav
%A Ghumashyan, Heghine
%T Strong endomorphism kernel property for finite Brouwerian semilattices and relative Stone algebras
%J Mathematica Bohemica
%D 2024
%P 13-25
%V 149
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2023.0050-22/
%R 10.21136/MB.2023.0050-22
%G en
%F 10_21136_MB_2023_0050_22
Guričan, Jaroslav; Ghumashyan, Heghine. Strong endomorphism kernel property for finite Brouwerian semilattices and relative Stone algebras. Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 13-25. doi: 10.21136/MB.2023.0050-22

[1] Blyth, T. S., Fang, J., Silva, H. J.: The endomorphism kernel property in finite distributive lattices and de Morgan algebras. Commun. Algebra 32 (2004), 2225-2242. | DOI | MR | JFM

[2] Blyth, T. S., Fang, J., Wang, L.-B.: The strong endomorphism kernel property in distributive double $p$-algebras. Sci. Math. Jpn. 76 (2013), 227-234. | DOI | MR | JFM

[3] Blyth, T. S., Silva, H. J.: The strong endomorphism kernel property in Ockham algebras. Commun. Algebra 36 (2008), 1682-1694. | DOI | MR | JFM

[4] Davey, B. A.: Dualities for equational classes of Brouwerian algebras and Heyting algebras. Trans. Am. Math. Soc. 221 (1976), 119-146. | DOI | MR | JFM

[5] Fang, G., Fang, J.: The strong endomorphism kernel property in distributive $p$-algebras. Southeast Asian Bull. Math. 37 (2013), 491-497. | MR | JFM

[6] Fang, J.: The strong endomorphism kernel property in double MS-algebras. Stud. Log. 105 (2017), 995-1013. | DOI | MR | JFM

[7] Fang, J., Sun, Z.-J.: Semilattices with the strong endomorphism kernel property. Algebra Univers. 70 (2013), 393-401. | DOI | MR | JFM

[8] Fang, J., Sun, Z. J.: Finite abelian groups with the strong endomorphism kernel property. Acta Math. Sin., Engl. Ser. 36 (2020), 1076-1082. | DOI | MR | JFM

[9] Ghumashyan, H., Guričan, J.: Endomorphism kernel property for finite groups. Math. Bohem. 147 347-358 (2022). | DOI | MR | JFM

[10] Grätzer, G.: Lattice Theory: Foundation. Birkhäuser, Basel (2011). | DOI | MR | JFM

[11] Guričan, J.: A note on the endomorphism kernel property. JP J. Algebra Number Theory Appl. 33 (2014), 133-139. | JFM

[12] Guričan, J.: Strong endomorphism kernel property for Brouwerian algebras. JP J. Algebra Number Theory Appl. 36 (2015), 241-258. | DOI | JFM

[13] Guričan, J., Ploščica, M.: The strong endomorphism kernel property for modular $p$-algebras and distributive lattices. Algebra Univers. 75 (2016), 243-255. | DOI | MR | JFM

[14] Halušková, E.: Strong endomorphism kernel property for monounary algebras. Math. Bohem. 143 (2018), 161-171. | DOI | MR | JFM

[15] Halušková, E.: Some monounary algebras with EKP. Math. Bohem. 145 (2020), 401-414. | DOI | MR | JFM

[16] Hashimoto, J.: Ideal theory for lattices. Math. Jap. 2 (1952), 149-186. | MR | JFM

[17] Hecht, T., Katriňák, T.: Equational classes of relative Stone algebras. Notre Dame J. Formal Logic 13 (1972), 248-254. | DOI | MR | JFM

[18] Katriňák, T.: Die Kennzeichnung der distributiven pseudokomplementären Halbverbände. J. Reine Angew. Math. 241 (1970), 160-179 German. | DOI | MR | JFM

[19] Katriňák, T.: Remarks on the W. C. Nemitz's paper 'Semi-Boolean lattices'. Notre Dame J. Formal Logic 11 (1970), 425-430. | DOI | MR | JFM

[20] Katriňák, T.: Relativ Stonesche Halbverbände sind Verbände. Bull. Soc. R. Sci. Liège 40 (1971), 91-93 German. | MR | JFM

[21] Katriňák, T.: Die Kennzeichnung der beschränkten Brouwerschen Verbände. Czech. Math. J. 22 (1972), 427-434 German. | DOI | MR | JFM

[22] Köhler, P.: Brouwerian semilattices. Trans. Am. Math. Soc. 268 (1981), 103-126. | DOI | MR | JFM

[23] Nemitz, W. C.: Implicative semi-lattices. Trans. Am. Math. Soc. 117 (1965), 128-142. | DOI | MR | JFM

[24] Ploščica, M.: Affine completions of distributive lattices. Order 13 (1996), 295-311. | DOI | MR | JFM

Cité par Sources :