Differentiation and splitting for lattices over orders (Q2717739)

The paper is a generalization of the author's paper [J. Pure Appl. Algebra 153, No. 2, 171-190 (2000; Zbl 0964.16016)], and is part of a project whose goal is to provide a module-theoretic approach to Zavadskij's differentiation techniques in representation theory [see \textit{A. G. Zavadskij}, Matrix problems, thematic Work Collect., Kiev 1977, 115-121 (1977; Zbl 0457.06001), Izv. Akad. Nauk SSSR, Ser. Mat. 55, No. 5, 1007-1048 (1991; Zbl 0809.16011), translation in Math. USSR, Izv. 39, No. 2, 975-1012 (1992), and \textit{A. G. Zavadskij, V. V. Kirichenko}, Mat. Sb., Nov. Ser. 103(145), 323-345 (1977; Zbl 0369.16004)]. The results of the paper imply the splitting theorem for vector space categories, namely, Theorem 17.53 of [\textit{D. Simson}, Linear representations of partially ordered sets and vector space categories. Algebra, Logic and Applications, 4. Gordon and Breach Science Publishers (1992; Zbl 0818.16009)].