No description available.

Let K be any field and Q be the rationals. Define K^1[X] = {f(X) e K[X]| the coefficient of X in f(X) is zero} and Q^1β[X] = {f(X) e Q[X]| the coefficent of β1(X) in the binomial expansion of f(X) is zero}, where {β1(X)}^∞ i=0 are the well-known binomial polynomials. In this work, I establish the following results: K^1[X] and Q^1β[X] are one-dimensional, Noetherian, non-Prüfer domains with the two-generator property on ideals. Using the unique factorization structure of the overrings K[X] and Q[X], the nonprincipal ideal structures of both rings are characterized, and from this characterization, necessary and sufficient conditions are found for a nonprincipal ideal to be invertible. The nonprincipal invertible ideals are then characterized in terms of the coefficients of the generators, and an explicit formula for the inverse of any proper invertible ideal is found. Finally, the class groups of both rings are shown to be torsion free abelian groups. Let n be any nonnegative integer. Results similar to the above are found in the generalizations of these two rings, K^n[X] and q^nβ[X], where the coefficients on the first n nonconstant basis elements are zero. For the domains K^1[X] and Q^1β[X], the property of strong two-generation is explored in detail and the following results are established: 1. K^1[X] and Q^1β[X] are not strongly two-generated, 2. In either ring, any polynomial with a constant term, or of degree two or three is a strong two-generator. 3. In K^1[X] any polynomial divisible by X^4 is not a strong two-generator, 4. An ideal I in K^1[X] or Q^1β[X] is strongly two-generated if and only if it is invertible.

abstract: Moral philosophy should create concepts and formulate arguments to articulate and assess the statements and behaviors of the morally devoted and the traditions (such as religious and ethical systems) founded by the morally devoted. Many moral devotees and their traditions advocate love as the ideal to live by. Therefore, moral philosophy needs an account of love as an ideal. I define an ideal as an instrument for organizing a life and show that this definition is more adequate than previous definitions. Ideals can be founded on virtues, and I show that love is a virtue. I define love as a composite attitude whose elements are benevolence, consideration, perception of moment (importance or significance), and receptivity. I define receptivity as the ability to be with someone without imposing careless or compulsive expectations. I argue that receptivity curbs the excesses and supplements the defects of the other elements. Love as an ideal is often understood as universal love. However, there are three problems with universal love: it could be too demanding, it could prevent intimacy and special relationships, and it could require a person to love their abuser. I argue that love can be extended to all human beings without posing unacceptable risks, once love is correctly defined and the ideal correctly understood. Because of the revelations of ecology and the ongoing transformation of sensibilities about the value of the nonhuman, love should be extended to the nonhuman. I argue that love can be given to the nonhuman in the same way it is to the human, with appropriate variations. But how much of the nonhuman would an ideal direct one to love? I argue for two limits to universal love: it does not make sense to extend it to nonliving things, and it can be extended to all living things. I show that loving all living things does not depend on whether they can reciprocate, and I argue that it would not prevent one from living a recognizably human life. / Dissertation/Thesis / Doctoral Dissertation Philosophy 2020

No description available.

The purpose of this paper will be to investigate certain properties of algebraic systems known as rings.

The purpose of this thesis is to investigate the properties of ideals in quadratic number fields, A field F is said to be an algebraic number field if F is a finite extension of R, the field of rational numbers. A field F is said to be a quadratic number field if F is an extension of degree 2 over R. The set 1 of integers of R will be called the rational integers.

The purpose of this thesis is to investigate certain properties of rings, ideals, and a special type of ring called a Boolean ring.

Let D be an integral domain and f a polynomial that is integer-valued on D. We prove that Int(f(D);D) has the Skolem Property and give a description of its spectrum. For certain discrete valuation domains we give a basis for the ring of integer-valued even polynomials. For these discrete valuation domains, we also give a series expansion of continuous integer-valued functions. / by Mario V. Marshall. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

by Ngai-ching Wong. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 197-201.

Thesis (Ph. D.)--University of Oregon, 2000. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 92-93). Also available for download via the World Wide Web; free to University of Oregon users.