The necessary and sufficient conditions are extracted for periodicity of bi-ideals. They cover infinitely and finitely generated bi-ideals.
@article{ITA_2008__42_3_467_0,
author = {Buls, J\=anis and Lorencs, Aivars},
title = {From bi-ideals to periodicity},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {42},
year = {2008},
pages = {467-475},
doi = {10.1051/ita:2008010},
mrnumber = {2434029},
zbl = {1149.68410},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2008__42_3_467_0}
}
Buls, Jānis; Lorencs, Aivars. From bi-ideals to periodicity. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) pp. 467-475. doi : 10.1051/ita:2008010. http://gdmltest.u-ga.fr/item/ITA_2008__42_3_467_0/
[1] , and . Avoidable patterns in strings of symbols. Pacific J. Math. 85 (1979) 261-294. | MR 574919 | Zbl 0428.05001
[2] , . Combinatorics on Words - A Tutorial. TUCS Technical Report (No. 530, June) (2003). | MR 1965433
[3] and . Une condition de finitude des monoïdes finiment engendrés. C.R. Acad. Sci. Paris, Sér. A 262 (1966) 1149-1151. | MR 194532 | Zbl 0141.01801
[4] and . Squares, cubes, and time-space efficient string searchinng. Algorithmica 13 (1995) 405-425. | MR 1323898 | Zbl 0849.68044
[5] , . (1965) Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR 174934 | Zbl 0131.30203
[6] . Algorithms on Strings, Trees, and Sequences. Cambridge University Press (1997). | MR 1460730 | Zbl 0934.68103
[7] . Structure of Rings. American Mathematical Society, Providence, RI (1964). | MR 222106 | Zbl 0073.02002
[8] . Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 17. Addison-Wesley, Reading, Massachusetts (1983). | MR 675953 | Zbl 0514.20045
[9] . Algebraic Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 90. Cambridge University Press, Cambridge (2002). | MR 1905123 | Zbl 1001.68093
[10] . Finiteness and Regularity in Semigroups and Formal Languages. Springer-Verlag, Berlin, Heidelberg (1999). | MR 1696498 | Zbl 0935.68056
[11] . Analysis and Design of Stream Ciphers. Springer-Verlag, Berlin (1986). | MR 861124 | Zbl 0618.94001
[12] . Infinite words and a theorem of Hindman. Rev. Math. Appl. 9 (1988) 97-104. | MR 950125 | Zbl 0711.05013
[13] . Data compression: methods and theory. Computer Science Press, Rockville, MD (1988).
[14] . Blocking sets of terms. Matem. sb., 119, 363-375 (Russian) (1982). | MR 678833 | Zbl 0599.20106