Pondělíček, Bedřich Semigroups whose proper one-sided ideals are t-Archimedean. (English) Zbl 0601.20055 Mat. Vesn. 37, 315-321 (1985). This paper studies semigroups for which certain classes of subsemigroups satisfy special constraints. If S is a semigroup, let \(a(S)\) be a collection of subsemigroups of S, e.g., \(a(S)=r(S)\), the collection of right ideals of S, or \(a(S)=\ell(S)\), the collection of left ideals of S. Let P be some fixed collection of semigroups, e.g., \(P=REG\), the collection of regular semigroups, or \(P=RAS\), the collection of right archimedean semigroups. Let \(P/a=\{S:\) \(a(S)\subseteq P\}\) and \(P/\bar a= \{S:\) \(a(S)\setminus \{S\}\subseteq P\}.\) This paper explores the relation between sets P and \(P/a\) or \(P/\bar a\) for various values of P and a. It culminates in the result that every proper one-sided ideal of a semigroup S is t-archimedean iff S satisfies one of the following conditions. 1. S is t-archimedean. 2. S is a semilattice of semigroups M and T, where M is a t-archimedean ideal of S and T a group whose identity is the identity of S. 3. S is a left (right) zero-semigroup of two groups. Reviewer: W.R.Nico Cited in 1 Document MSC: 20M10 General structure theory for semigroups 20M12 Ideal theory for semigroups Keywords:subsemigroups; right ideals; left ideals; regular semigroups; right archimedean semigroups; semilattice of semigroups PDFBibTeX XMLCite \textit{B. Pondělíček}, Mat. Vesn. 37, 315--321 (1985; Zbl 0601.20055)