The classical ring of integer-valued polynomials Int(Z) consists of the polynomials in Q[X] that map Z into Z. We consider a generalization of integervalued polynomials where elements of Q[X] act onâ€¦ (More)

In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer's book [20]) and, hence, the relatedâ€¦ (More)

Reference departments track patron interactions to illustrate the type and number of services provided as well as to tailor librarians' time and expertise to the interest and needs of their patrons.â€¦ (More)

We give a classification of e.a.b. semistar (and star) operations by defining four different (successively smaller) distinguished classes. Then, using a standard notion of equivalence of semistarâ€¦ (More)

Let R be a commutative ring and let Spec(R) denote the collection of prime ideals of R. We define a topology on Spec(R) by using ultrafilters and demonstrate that this topology is identical to theâ€¦ (More)

We prove that the theory of root closed monoids is axiomatizable, but not finitely axiomatizable. Some directions for further research are presented. All monoids in this paper are assumedâ€¦ (More)