Abstract. Let R and S be two rings. Each category equivalence between a torsion class of left (right) R-modules and a torsion-free class of left (right) S- modules is represented by a left (right) quasi-tilting triple. Suppose we have a −→ −→ pair of equivalences T ←− Y and X ←− F, between the torsion class T of R- modules and the torsion-free class Y of S-modules and between the torsion class X of S-modules and the torsion-free class F of R-modules. Denote by (R, V, S) and (S, U, R) the quasi-tilting triples representing these equivalences. We say that (R,V,S) and (S,U,R) are complementary if (T ,F) and (X,Y) are torsion theories in R-Mod and S-Mod, respectively. We find necessary and sufficient conditions on the bimodules RVS and SUR to have the complementarity of (R,V,S) and (S, U, R).
On the complementarity of two quasi-tilting triples
TONOLO, ALBERTO
2001
Abstract
Abstract. Let R and S be two rings. Each category equivalence between a torsion class of left (right) R-modules and a torsion-free class of left (right) S- modules is represented by a left (right) quasi-tilting triple. Suppose we have a −→ −→ pair of equivalences T ←− Y and X ←− F, between the torsion class T of R- modules and the torsion-free class Y of S-modules and between the torsion class X of S-modules and the torsion-free class F of R-modules. Denote by (R, V, S) and (S, U, R) the quasi-tilting triples representing these equivalences. We say that (R,V,S) and (S,U,R) are complementary if (T ,F) and (X,Y) are torsion theories in R-Mod and S-Mod, respectively. We find necessary and sufficient conditions on the bimodules RVS and SUR to have the complementarity of (R,V,S) and (S, U, R).Pubblicazioni consigliate
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