Affiliation:
1. University of Szeged Bolyai Institute Aradi vértanúk tere 1 6720 Szeged HUNGARY URL:
2. P. J. Šafárik University Institute of Mathematics Jesenná 5 04154 Košice SLOVAKIA
Abstract
Abstract
Let τ be a nonempty similarity type of algebras. A set H of τ-algebras is called rigid with respect to embeddability, if whenever A, B ∈ H and φ: A → B is an embedding, then A = B and φ is the identity map. We prove that if τ is a nonempty similarity type and 𝖒 is a cardinal such that no inaccessible cardinal is smaller than or equal to m, then there exists a set H of τ-algebras such that H is rigid with respect to embeddability and |H| = 𝖒. This result strengthens a result proved by the second author in 1980.
Reference10 articles.
1. Comer, S. D.—Le Tourneau, J. J.: Isomorphism types of infinite algebras, Proc. Amer. Math. Soc. 21 (1969), 635–639.
2. Farkasová, Z.—Jakubíková-Studenovská, D.: Polymorphism-homogeneous monounary algebras, Math. Slovaca 65 (2015), 359–370.
3. Halusková, E.: On inverse limits of monounary algebras, Math. Slovaca 64 (2014), 691–706.
4. Horváth, G.—Kátai-Urbán, K.—Pach, P. P.—Pongrácz, A.—Pluhár, G.—Szabó O, CS.: The number of monounary algebras, Algebra Universalis 66 (2011), 81–83.
5. Jakubíková-Studenovská, D.: On weakly rigid monounary algebras, Math. Slovaca 30 (1980), 197–206.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献