Geodesic
Closure operators in the categories of modules. Part~III (Operations in 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 CO of all closure operators of a`module category R-Mod. The principal operations in 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. https://geodesic-test.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