Jakubíková-Studenovská, Danica; Pócs, Jozef Formations of finite monounary algebras. (English) Zbl 1283.08006 Algebra Univers. 68, No. 3-4, 249-255 (2012). The notion of a formation algebra has been firstly introduced in 1970s for finite groups. After that, this concept was deeply investigated for the cases of lattices, \(\ell\)-groups, GMV-algebras and general algebraic structures. In this paper, the authors prove that the collection of all formations of finite monounary algebras is isomorphic to the lattice of all hereditary subsets of a certain poset. Reviewer: Lavinia Ciungu (Craiova) Cited in 8 Documents MSC: 08A60 Unary algebras 08B26 Subdirect products and subdirect irreducibility Keywords:monounary algebra; formation; subdirect product; formation algebra PDFBibTeX XMLCite \textit{D. Jakubíková-Studenovská} and \textit{J. Pócs}, Algebra Univers. 68, No. 3--4, 249--255 (2012; Zbl 1283.08006) Full Text: DOI References: [1] Jakubík J.: Formations of lattice ordered groups and GMV-algebras. Math. Slovaca 58, 521–534 (2008) · Zbl 1199.06068 · doi:10.2478/s12175-008-0091-2 [2] Jakubíková-Studenovská D.: On completions of partial monounary algebras. Czechoslovak Math. J. 38(113), 256–268 (1988) · Zbl 0659.08003 [3] Jakubíková-Studenovská D., Pócs J.: Monounary Algebras. Pavol Jozef Šafárik University, Košice (2009) [4] Lihová J., Pócs J.: On formations of lattices. Acta Univ. M. Belii Ser. Math. 15, 63–72 (2009) · Zbl 1203.06009 [5] Marica J.G., Bryant S.J.: Unary algebras. Pacific J. Math. 10, 1347–1359 (1960) · Zbl 0163.26501 · doi:10.2140/pjm.1960.10.1347 [6] McKenzie R.: Cardinal multiplication of structures with a reflexive relation. Fund. Math. 70, 59–101 (1971) · Zbl 0228.08002 [7] Shemetkov, L.A.: Formations of Finite Groups. Nauka, Moskva (1978) (Russian) · Zbl 0496.20014 [8] Shemetkov, L.A., Skiba, A.N.: Formations of Algebraic Systems. Nauka, Moskva (1989) (Russian) · Zbl 0667.08001 [9] Shemetkov L.A., Skiba A.N., Vorob’ev N.N.: On laws of lattices of partially saturated formations. Asian-Eur. J. Math. 2, 155–169 (2009) · Zbl 1217.20007 · doi:10.1142/S1793557109000133 [10] Shemetkov L.A., Skiba A.N., Vorob’ev N.N.: On lattices of formations of finite groups. Algebra Colloq. 17, 557–564 (2010) · Zbl 1211.20020 [11] Wenzel G.H.: Subdirect irreducibility and equational compactness in unary algebras $${\(\backslash\)langle A; f \(\backslash\)rangle}$$ . Arch. Math. 21, 256–264 (1970) · Zbl 0207.02902 · doi:10.1007/BF01220912 [12] Yoeli M.: Subdirectly irreducible unary algebras. Amer. Math. Monthly 74, 957–960 (1967) · Zbl 0153.33802 · doi:10.2307/2315275 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.