separative ideals of exchange rings

Separative Ideals of Exchange Rings

Of Separative Exchange Rings Andc * - Algebras with Real Rank Zerop

For any (unital) exchange ring R whose nitely generated projective modules satisfy the separative cancellation property (A A = A B = B B =) A = B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL 1 (R) ! K 1 (R) is surjective. In combination with a result of Huaxin Lin, it follows that ...

Separative Exchange Rings and C * - Algebras with Real Rank Zero

For any (unital) exchange ring R whose finitely generated projective modules satisfy the separative cancellation property (A ⊕ A ∼= A ⊕ B ∼= B ⊕ B =⇒ A ∼= B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL1(R) → K1(R) is surjective. In combination with a result of Huaxin Lin, it follow...

Of Separative Exchange Rings and C * - Algebras with Real Rank Zero

For any (unital) exchange ring R whose finitely generated projective modules satisfy the separative cancellation property (A ⊕ A ∼= A ⊕ B ∼= B ⊕ B =⇒ A ∼= B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL1(R) → K1(R) is surjective. In combination with a result of Huaxin Lin, it follow...

On $z$-ideals of pointfree function rings

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

Ideals in Computable Rings

We show that the existence of a nontrivial proper ideal in a commutative ring with identity which is not a eld is equivalent to WKL0 over RCA0, and that the existence of a nontrivial proper nitely generated ideal in a commutative ring with identity which is not a eld is equivalent to ACA0 over RCA0. We also prove that there are computable commutative rings with identity where the nilradical is ...