A module M is ⊕-supplemented if every submodule of M has a supplement which is a direct summand of M. In this paper, we show that a quotient of a ⊕-supplemented module is not in general ⊕-supplemented. We prove that over a commutative ring R, every finitely generated ⊕-supplemented R-module M having dual Goldie dimension less than or equal to three is a direct sum of local modules. It is also shown that a ring R is semisimple if and only if the class of ⊕-supplemented R-modules coincides with the class of injective R-modules. The structure of ⊕-supplemented modules over a commutative principal ideal ring is completely determined.2000 Mathematics Subject Classification: 16D50, 16D60, 13E05, 13E15, 16L60, 16P20, 16D80. Introduction.All rings considered in this paper will be associative with an identity element. Unless otherwise mentioned, all modules will be left unitary modules. Let R be a ring and M an R-module. Let A and P be submodules of M. The submodule P is called a supplement of A if it is minimal with respect to the property A + P = M. Any L ≤ M which is the supplement of an N ≤ M will be called a supplement submodule of M. If every submodule U of M has a supplement in M, we call M complemented. In [25, page 331], Zöschinger shows that over a discrete valuation ring R, every complemented R-module satisfies the following property (P ): every submodule has a supplement which is a direct summand. He also remarked in [25, page 333] that every module of the form M (R/a 1 ) × ··· × (R/a n ), where R is a commutative local ring and a i (1 ≤ i ≤ n) are ideals of R, satisfies (P ). In [12, page 95], Mohamed and Müller called a module ⊕-supplemented if it satisfies property (P ).On the other hand, let U and V be submodules of a module M. The submodule V is called a complement of U in M if V is maximal with respect to the property V ∩U = 0. In [17] Smith and Tercan investigate the following property which they called (C 11 ): every submodule of M has a complement which is a direct summand of M. So, it was natural to introduce a dual notion of (C 11 ) which we called (D 11 ) (see [6,7]). It turns out that modules satisfying (D 11 ) are exactly the ⊕-supplemented modules. A module M is called a completely ⊕-supplemented (see [5]) (or satisfies (D

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Resumen: Esta crónica recoge las conclusiones y refl exiones principales del Seminario Hispano-Marroquí sobre Turismo Responsable, Medio Ambiente y Desarrollo Sostenible en Espacios Rurales y Naturales organizado en Tetuán (Marruecos) en diciembre de 2011 en el marco del programa de cooperación interuniversitaria e investigación científi ca (PCI) denominado "Gestión del Turismo Responsable y Solidario y Desarrollo Territorial Sostenible", fi nanciado por la Agencia Española de Cooperación Internacional para el Desarrollo (AECID) y puesto en marcha por las Universidades de Córdoba (España) y Abdelmalek Essaâdi (Marruecos). Además del análisis de los resultados conseguidos sobre conceptualización del turismo responsable, análisis de experiencias de buenas prácticas y defi nición de estrategias y actuaciones necesarias de cara al futuro, se transcribe en este trabajo el texto completo de la declaración fi nal del Seminario elaborada por el grupo de expertos participantes, entre los que se encuentran los autores de esta reseña.Palabras clave: Turismo ético y responsable; Espacios rurales y naturales; Erradicación de la pobreza; Países en vías de desarrollo.

A module [Formula: see text] is called coseparable ([Formula: see text]-coseparable) if for every submodule [Formula: see text] of [Formula: see text] such that [Formula: see text] is finitely generated ([Formula: see text] is simple), there exists a direct summand [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text] is finitely generated. In this paper, we show that free modules are coseparable. We also investigate whether or not the ([Formula: see text]-)coseparability is stable under taking submodules, factor modules, direct summands, direct sums and direct products. We show that a finite direct sum of coseparable modules is not, in general, coseparable. But the class of [Formula: see text]-coseparable modules is closed under finite direct sums. Moreover, it is shown that the class of coseparable modules over noetherian rings is closed under finite direct sums. A characterization of coseparable modules over noetherian rings is provided. It is also shown that every lifting (H-supplemented) module is coseparable ([Formula: see text]-coseparable).

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