Previous |  Up |  Next

Article

Keywords:
monounary algebra; direct limit; endomorphism; retract
Summary:
In this paper we describe all algebras $A$ with one unary operation such that by a direct limit construction exactly two nonisomorphic algebras can be obtained from $A$.
References:
[1] J. Adámek J. Rosický: Locally Presentable and Аccessible Categories. Cambridge University-Press, 1994. MR 1294136
[2] G. Grätzer: Universal Аlgebra. Springer-Verlag, New York, 1979. MR 0538623
[3] E. Halušková: On iterated direct limits of a monounary algebra. Contributions to general algebra, 10 (Klagenfurt, 1997). Heyn, Klagenfurt, 1998, pp. 189-195. MR 1648786
[4] E. Halušková: Direct limits of monounary algebras. Czechoslovak Math. J. 49 (1999), 645-656. DOI 10.1023/A:1022435806014 | MR 1708334
[5] D. Jakubíková-Studenovská: Retract irreducibìlity of connected monounary algebras I, II. Czechoslovak Math. J 46 (1996), 291-307; 47 (1997), 113-126. MR 1388617
[6] D. Jakubíková-Studenovská: Two types of retract irreducibility of connected monounary algebras. Math. Bohem. 121 (1996), 143-150. MR 1400606
[7] D. Jakubíková-Studenovská: DR-irreducibility of connected monounary algebras with a cycle. Submitted to Czechoslovak Math. J. MR 1792964
[8] D. Jakubíková-Studenovská: DR-irreducibility of connected monounary algebras. To appear in Czechoslovak Math. J. MR 1792966
[9] B. Jónsson: Topics in Universal Аlgebra. Lect. Notes Math. 250, Springer-Verlag, Berlin, 1972. DOI 10.1007/BFb0058648
[10] M. Novotný: Über Аbbildungen von Mengen. Pacific J. Math. 13 (1963), 1359-1369. DOI 10.2140/pjm.1963.13.1359
Partner of
EuDML logo