Geodesic
The pre-period of the glued sum of finite modular lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 223-231.

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

The notion of a pre-period of an algebra 𝐀 is defined by means of the notion of the pre-period λ(f) of a monounary algebra 〈 A;f〉: it is determined by sup{λ(f)| f is an endomorphism of 𝐀}. In this paper we focus on the pre-period of a finite modular lattice. The main result is that the pre-period of any finite modular lattice is less than or equal to the length of the lattice; also, necessary and sufficient conditions under which the pre-period of the glued sum is equal to the length of the lattice, are shown. Moreover, we show the triangle inequality of the pre-period of the glued sum.
Keywords: ordinal sum, glued sum, modular lattice, endomorphism, pre-period, connected unary operation 
@article{DMGAA_2023_43_2_a3,
     author = {Charoenpol, Aveya and Chotwattakawanit, Udom},
     title = {The pre-period of the glued sum of finite modular lattices},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {223--231},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a3/}
}
TY  - JOUR
AU  - Charoenpol, Aveya
AU  - Chotwattakawanit, Udom
TI  - The pre-period of the glued sum of finite modular lattices
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2023
SP  - 223
EP  - 231
VL  - 43
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a3/
LA  - en
ID  - DMGAA_2023_43_2_a3
ER  - 
%0 Journal Article
%A Charoenpol, Aveya
%A Chotwattakawanit, Udom
%T The pre-period of the glued sum of finite modular lattices
%J Discussiones Mathematicae. General Algebra and Applications
%D 2023
%P 223-231
%V 43
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a3/
%G en
%F DMGAA_2023_43_2_a3
Charoenpol, Aveya; Chotwattakawanit, Udom. The pre-period of the glued sum of finite modular lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 223-231. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a3/

[1] U. Chotwattakawanit and A. Charoenpol, A pre-period of a finite distributive lattice, Discuss. Math. General Alg. Appl. (to appear).

[2] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science (Chapman & Hall, CRC Press, Boca Raton, London, New York, Washington DC, 2002).

[3] E. Halukova, Strong endomorphism kernel property for monounary algebras, Math. Bohemica 143 (2017) 1–11.

[4] E. Halukova, Some monounary algebras with EKP, Math. Bohemica 145 (2019) 1–14. https://doi.org/10.21136/MB.2017.0056-16

[5] D. Jakubikova-Studenovska, Homomorphism order of connected monounary algebras, Order 38 (2021) 257–269. https://doi.org/10.1007/s11083-020-09539-y

[6] D. Jakubikova-Studenovska and J. Pocs, Monounary algebras (P.J. Safarik Univ. Kosice, Kosice, 2009).

[7] D. Jakubikova-Studenovska and K. Potpinkova, The endomorphism spectrum of a monounary algebra, Math. Slovaca 64 (2014) 675–690. https://doi.org/10.2478/s12175-014-0233-7

[8] B. Jonsson, Topics in Universal Algebra (Lecture Notes in Mathematics 250, Springer, Berlin, 1972).

[9] M. Novotna, O. Kopeek and J. Chvalina, Homomorphic Transformations: Why and Possible Ways to How (Masaryk University, Brno, 2012).

[10] J. Pitkethly and B. Davey, Dualisability: Unary Algebras and Beyond (Advances in Mathematics 9, Springer, New York, 2005).

[11] B.V. Popov and O.V. Kovaleva, On a characterization of monounary algebras by their endomorphism semigroups, Semigroup Forum 73 (2006) 444–456. https://doi.org/10.1007/s00233-006-0635-0

[12] I. Pozdnyakova, Semigroups of endomorphisms of some infinite monounary algebras, J. Math. Sci. 190 (2013). https://doi.org/10.1007/s10958-013-1278-9

[13] C. Ratanaprasert and K. Denecke, Unary operations with long pre-periods, Discrete Math. 308 (2008) 4998–5005. https://doi.org/10.1142/S1793557109000170

[14] H. Yoeli, Subdirectly irreducible unary algebra, Math. Monthly 74 (1967) 957–960. https://doi.org/10.2307/2315275

[15] D. Zupnik, Cayley functions, Semigroup Forum 3 (1972) 349–358. https://doi.org/10.1007/BF02572972