Mono-unary condition for algebras with easy direct limits
DOI:
https://doi.org/10.64700/altay.5Keywords:
Algebra, direct limit, retract, operation, endomorphismAbstract
Let \(\mathcal{A}\) be an algebra such that exactly algebras isomorphic to a retract of \(\mathcal{A}\) can be constructed from \(\mathcal{A}\) by direct limits. One condition which is satisfied for \(\mathcal{A}\) in the case that \(\mathcal{A}\) has a unary term operation which is an endomorphism of \(\mathcal{A}\) at the same time is presented. A bijective mapping occurs in this condition and mono-unary algebras are used substantially.
References
[1] J. Berman, P. M. Idziak: Generative Complexity in Algebra, Memoirs of the AMS, 175. Amer. Math. Soc., Providence (2005).
[2] G. Grätzer: Universal Algebra, The University Series in Higher Mathematics, D. Van Nostrand, Co., Princeton, New York, (1968).
[3] E. Halušková: On iterated direct limits of a monounary algebra, Contributions to general algebra 10, 189-195, Heyn, Klagenfurt (1998).
[4] E. Halušková: Direct limits of monounary algebras, Czechoslovak Math. J., 49 (1999), 645-656.
[5] E. Halušková: Monounary algebras with easy direct limits, Miskolc Math. Notes, 19(1) (2018), 291–302.
[6] E. Halušková, M. Plošˇcica: On direct limits of finite algebras, Contributions to general algebra 11, 101-104, Heyn, Klagenfurt (1999).
[7] J. Jakubík, G. Pringerová: Direct limits of cyclically ordered groups, Czechoslovak Math. J., 44 (1994), 231-250.
[8] D. Jakubíková-Studenovská, J. Pócs: Cardinality of retracts of monounary algebras, Czechoslovak Math. J., 58(2) (2008), 469-479.
[9] D. Jakubíková-Studenovská, J. Pócs: Monounary algebras, P. J. Šafárik University in Košice (2009).
[10] B. Jónsson: Topics in universal algebra, Lecture Notes in Mathematics 250, Springer-Verlag, Berlin-Heidelberg-New York (1972).
[11] T.Y. Lam: A First Course in Noncommutative Rings, Springer-Verlag: New York (1991).
[12] R. Schmidt: Subgruop lattices of groups, Expositions in Math. 14, de Gruyter (1994).
[13] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties 1,Wadsworth (1987).
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