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- Title
Baer duality for commutative rings.
- Authors
Ánh, Pham Ngoc; Herbera, Dolors; Menini, Claudia
- Abstract
A Baer duality is a triple (R, [subR]U[subT], T), consisting of rings R, T and a bimodule [subR]U[subT] faithful on both sides, such that the lattices of submodules L ([subR]R) and L(U[subT]), as well as L([subR]U) and L(T[subT]), are anti-isomorphic. The theory of Baer duality for commutative rings is developed. Analogously to the Morita duality case, it is shown that any commutative ring with Baer duality has self-duality. The existence of the lattice anti-isomorphisms in a Baer duality implies that all the lattices involved satisfy Grothendieck's condition AB5*. It is showed that any AB5* commutative domain has Baer duality. An example of an AB5* commutative ring without Baer duality is given.
- Subjects
DUALITY theory (Mathematics); COMMUTATIVE rings; RING theory; ALGEBRA
- Publication
Forum Mathematicum, 2002, Vol 14, Issue 1, p47
- ISSN
0933-7741
- Publication type
Article