Flatness properties of acts over semigroups | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 4، دوره 15، شماره 1، مهر 2021، صفحه 59-92 اصل مقاله (782.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.52547/cgasa.15.1.59 | ||
| نویسندگان | ||
| Valdis Laan1؛ Ülo Reimaa2؛ Lauri Tart2؛ Elery Teor3 | ||
| 1Institute of Mathematics and Statistics, University of Tartu, Tartu, Estonia. | ||
| 2Institute of Mathematics and Statistics, University of Tartu, Tartu, Estonia | ||
| 3Hotel Tartu, Tartu, Estonia. | ||
| چکیده | ||
| In this paper we study flatness properties (pullback flatness, limit flatness, finite limit flatness) of acts over semigroups. These are defined by requiring preservation of certain limits from the functor of tensor multiplication by a given act. We give a description of firm pullback flat acts using Conditions (P) and (E). We also study pure epimorphisms and their connections to finitely presented acts and pullback flat acts. We study these flatness properties in the category of all acts, as well as in the category of unitary acts and in the category of firm acts, which arise naturally in the Morita theory of semigroups. | ||
| کلیدواژهها | ||
| Act over semigroup؛ pullback flatness؛ finite limit flatness؛ pure epimorphism؛ finitely presentable act؛ firm act؛ sequence act | ||
| مراجع | ||
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