Lattice operations on Rickart ∗-rings under the star order

Minus Partial Order in Rickart Rings

The minus partial order is already known for complex matrices and bounded linear operators on Hilbert spaces. We extend this notion to Rickart rings, and thus we generalize some well-known results.

Note on Star Operations over Polynomial Rings

This paper studies the notions of star and semistar operations over a polynomial ring. It aims at characterizing when every upper to zero in R[X] is a ∗-maximal ideal and when a ∗-maximal ideal Q of R[X] is extended from R, that is, Q = (Q ∩ R)[X] with Q ∩R 6= 0, for a given star operation of finite character ∗ on R[X]. We also answer negatively some questions raised by Anderson-Clarke by const...

Note on the Star Operations over Polynomial Rings

This paper studies the notion of star and semistar operations over a polynomial ring. It aims at characterizing when every upper to zero in R[X] is a ∗-maximal ideal and when a ∗-maximal ideal Q of R[X] is extended from R, that is, Q = (Q ∩ R)[X] with Q ∩R 6= 0, for a given star operation of finite character ∗ on R[X]. We also answer negatively some questions raised by Anderson-Clarke by constr...

An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations

On the Spectral Theory for Rickart Ordered

RO-algebras are defined and studied. For RO-algebra T , using properties of partial order, it is established that the set of bounded elements can be endowed with C-norm. The structure of commutative subalgebras of T is considered and the Spectral Theorem for any self-adjoint element of T is proven.