TY - GEN

T1 - Remarks on representations of universal algebras by sheaves of quotient algebras

AU - Johnson, Michael

AU - Sun, Shu-Hao

PY - 1992

Y1 - 1992

N2 - Nontrivial sheaf representation theorems are known for the class of algebras whose congruence lattices are distributive and the class whose congruence lattices are normal unital quantales, which include Keimel's representations of F-rings and Cornish's representations of normal lattices. Unfortunately such results do not include the sheaf representation theorems for rings with identity. In this paper, a sheaf representation for a class of universal algebras with congruence lattice containing a particular type of subframe is presented. As a consequence a representation of non commutative rings is given. This solves a problem posed by A. Wolf [in Recent advances in the representation theory of rings and C∗-algebras by continuous sections (New Orleans, LA, 1973), 87–93, Mem. Amer. Math. Soc., 148, Amer. Math. Soc., Providence, RI, 1974; MR0369223], but it does not yield Grothendieck representations, nor some of the representations of J. Lambek [Canad. Math. Bull. 14 (1971), 359–368; MR0313324].

AB - Nontrivial sheaf representation theorems are known for the class of algebras whose congruence lattices are distributive and the class whose congruence lattices are normal unital quantales, which include Keimel's representations of F-rings and Cornish's representations of normal lattices. Unfortunately such results do not include the sheaf representation theorems for rings with identity. In this paper, a sheaf representation for a class of universal algebras with congruence lattice containing a particular type of subframe is presented. As a consequence a representation of non commutative rings is given. This solves a problem posed by A. Wolf [in Recent advances in the representation theory of rings and C∗-algebras by continuous sections (New Orleans, LA, 1973), 87–93, Mem. Amer. Math. Soc., 148, Amer. Math. Soc., Providence, RI, 1974; MR0369223], but it does not yield Grothendieck representations, nor some of the representations of J. Lambek [Canad. Math. Bull. 14 (1971), 359–368; MR0313324].

M3 - Conference proceeding contribution

SN - 9780821860182

T3 - Canadian Mathematical Society

SP - 299

EP - 307

BT - Category Theory 1991

A2 - Seely, R. A. G.

PB - Canadian Mathematical Society

ER -