3 citations · 3 across the 6 of their papers we have counts for
6 papers
Adjoining Idempotents to a Commutative Ring preprint version
W. D. Burgess, R. Raphael
Everything takes place in the category of commutative unitary rings. For a fixed ring , $\alg{R}$ is the class of -algebras and $\igr{R}$ the subclass of idempotent generated…
On extending C^k functions from an open set to R, with applications
W. D. Burgess, R. Raphael
For and open in , let $\C^{\,k}(U)$ be the ring of real valued functions on with the first derivatives continuous. It is shown for $f\in \…
The reduced ring order and lower semi-lattices II
W. D. Burgess, R. Raphael
This paper continues the study of the reduced ring order (rr-order) in reduced rings where if . A reduced ring is called rr-good if it is a lower semi-lattice in th…
Tychonoff spaces and a ring theoretic order on
W. D. Burgess, R. Raphael
The reduced ring order (rr-order) is a natural partial order on a reduced ring given by if . It can be studied algebraically or topologically in ri…
The reduced ring order and lower semi-lattices
W. D. Burgess, R. Raphael
Every reduced ring has a natural partial order defined by if ; it generalizes the natural order on a boolean ring. The article examines when is a lower sem…
On strongly clean matrices over commutative clean rings
Walter Burgess
The literature about strongly clean matrices over commutative rings is quite extensive. The sharpest results are about matrices over commutative local rings, for example those by B…