Geodesic
Closure operators in the categories of modules. Part~III (Operations in $\mathbb{CO}$ and their properties)
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2014), pp. 90-100.

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This article is a continuation of the works [1] and [2] (Part I and Part II) and contains some results on the family $\mathbb{CO}$ of all closure operators of a`module category $R$-Mod. The principal operations in $\mathbb{CO}$ (meet, join, product, coproduct) are studied and their properties are elucidated. Also the question on the preservation of types of closure operators with respect to these operations is investigated. 
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A. I. Kashu. Closure operators in the categories of modules. Part~III (Operations in $\mathbb{CO}$ and their properties). Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2014), pp. 90-100. http://geodesic.mathdoc.fr/item/BASM_2014_1_a5/

[1] Kashu A. I., “Closure operators in the categories of modules. Part I. Weakly hereditary and idempotent operators”, Algebra and Discrete Mathematics, 15:2 (2013), 213–228 | MR

[2] Kashu A. I., “Closure operators in the categories of modules. Part II. Hereditary and cohereditary operators”, Algebra and Discrete Mathematics, 16:1 (2013), 81–95 | MR

[3] Dikranjan D., Giuli E., “Factorizations, injectivity and compactness in categories of modules”, Commun. in Algebra, 19:1 (1991), 45–83 | DOI | MR | Zbl

[4] Dikranjan D., Giuli E., “Closure operators. I”, Topology and its Applications, 27 (1987), 129–143 | DOI | MR | Zbl

[5] Dikranjan D., Tholen W., Categorical structure of closure operators, Kluwer Academic Publishers, 1995 | MR | Zbl

[6] Kashu A. I., “Radical closures in categories of modules”, Mat. Issled. (Kishinev), 5:4(18) (1970), 91–104 (in Russian) | MR | Zbl