On equimultiple ideals.
On equimultiple subschemes of a local scheme over a field of characteristic zero
On Euclidean Algorithms With Some Particular Properties
On exact modules over a commutative exact ring
On extending functions from an open set to with applications
For and open in , let be the ring of real valued functions on with the first derivatives continuous. It is shown that for there is with and with . The function and its derivatives are not assumed to be bounded on . The function is constructed using splines based on the Mollifier function. Some consequences about the ring are deduced from this, in particular that .
On extensions of partial -operators
On -rings that are not formally real
Henriksen and Isbell showed in 1962 that some commutative rings admit total orderings that violate equational laws (in the language of lattice-ordered rings) that are satisfied by all totally-ordered fields. In this paper, we review the work of Henriksen and Isbell on this topic, construct and classify some examples that illustrate this phenomenon using the valuation theory of Hion (in the process, answering a question posed in [E]) and, finally, prove that a base for the equational theory of totally-ordered...
On Factorization into Prime Ideals
On finite algebras projectively represented by graded complete intersections.
On Finite Conductor Domains.
On finite principal ideal rings.
On finitely generated birational flat extensions of integral domains
On finitely generated multiplication ideals in commutative rings
On finitely generated multiplication modules
We shall prove that if is a finitely generated multiplication module and is a finitely generated ideal of , then there exists a distributive lattice such that with Zariski topology is homeomorphic to to Stone topology. Finally we shall give a characterization of finitely generated multiplication -modules such that is a finitely generated ideal of .
On Form Ideals and Artin-Rees Condition.
On formal groups over complete discrete valuation rings with application to a theorem of Lutz.
On Gaussian polynomials and content ideal.
On generalized derivations of partially ordered sets
Let be a poset and be a derivation on . In this research, the notion of generalized -derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized -derivations are introduced. The properties of the fixed points based on the generalized -derivations are examined. The properties of ideals and operations related with generalized -derivations are studied.
On generalized quaternion algebras.
On generalized Redei functions.