Sums of Semiprime, Z, and D L-Ideals in a Class of F-Rings

In this paper it is shown that there is a large class of f-rings in which the sum of any two semiprime i-ideals is semiprime. This result is used to give a class of commutative f-rings with identity element in which the sum of any two z-ideals which are i-ideals is a z-ideal and the sum of any two d-ideals is a d-ideal

When is Every Order Ideal a Ring Ideal?

A lattice-ordered ring R is called an OIRI-ring if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f-rings R such that R/I is contained in an f-ring with an identity element that is a strong order unit for some nil l-ideal I of R. In particular, if P(R) denotes the set of nilpotent elements of the f-ring R, then R is an OIRI-ring if and only if R/P(R) is contained in an f-ring with an identity element that is a strong order unit

Pseudoprime L-Ideals in a Class of F-Rings

In a commutative f-ring, an l-ideal I is called pseudoprime if ab = 0 implies a ∈ I or b ∈ I, and is called square dominated if for every a ∈ I, |a| ≤ x2 for some x ∈ A such that x2 ∈ I. Several characterizations of pseudoprime l-ideals are given in the class of commutative semiprime f-rings in which minimal prime l-ideals are square dominated. It is shown that the hypothesis imposed on the f-rings, that minimal prime l-ideals are square dominated, cannot be omitted or generalized

Finitely 1-convex f-rings

This paper investigates f-rings that can be constructed in a finite number of steps where every step consists of taking the fibre product of two f-rings, both being either a 1-convex f-ring or a fibre product obtained in an earlier step of the construction. These are the f-rings that satisfy the algebraic property that rings of continuous functions possess when the underlying topological space is finitely an F-space (i.e. has a Stone-čech compactification that is a finite union of compact F-spaces). These f-rings are shown to be SV f-rings with bounded inversion and finite rank and, when constructed from semisimple f-rings, their maximal ideal space under the hull-kernel topology contains a dense open set of maximal ideals containing a unique minimal prime ideal. For a large class of these rings, the sum of prime, semiprime, primary and z-ideals are shown to be prime, semiprime, primary and z-ideals respectively

Humboldt State University: 1982 Convention Site/June 16-20, 1982

Humboldt State University shares the delight of its Women\u27s Studies Program that the National Women\u27s Studies Association is bringing its 1982 Convention to our campus. University staff and faculty are working together on arrangements that will encourage women\u27s studies practitioners from all over the country to come to Humboldt. HSU\u27s excellent interdisciplinary Women\u27s Studies Program, founded in 1970, is sponsored by several departments, including English, Economics, Ethnic Studies, History, Physical Education, Political Science, Psychology, Sociology, Speech Communication, and Art. Approximately 20 faculty members offer some 30 courses. The Program contributes to General Education at Humboldt through courses in Women and the Artistic Response, Historical Views of Women, Women in Language and Literature, Women in Social Institutions, and Psychological Views of Women. It offers a minor in Women\u27s Studies, and students can major in Women\u27s Studies through the Special Major Program

Lattice-Ordered Algebras That are Subdirect Products of Valuation Domains

An f-ring (i.e., a lattice-ordered ring that is a subdirect product of totally ordered rings) A is called an SV-ring if A/P is a valuation domain for every prime ideal P of A. If M is a maximal ℓ-ideal of A , then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal ℓ-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A = C(X) is the ring of all real-valued continuous functions on a Tychonoff space, the rank of X is defined to be the rank of the f-ring C(X), and X is called an SV-space if C(X) is an SV-ring. X has finite rank k iff k is the maximal number of pairwise disjoint cozero sets with a point common to all of their closures. In general f-rings these two concepts are unrelated, but if A is uniformly complete (in particular, if A = C(X)) then if A is an SV-ring then it has finite rank. Showing that ihis latter holds makes use of the theory of finite-valued lattice-ordered (abelian) groups. These two kinds of rings are investigated with an emphasis on the uniformly complete case. Fairly powerful machinery seems to have to be used, and even then, we do not know if there is a compact space X of finite rank that fails to be an SV-space

Measurement of Organizational Culture and Climate in Healthcare

Although there is increasing interest in the relationship between organizational constructs and health services outcomes, information on the reliability and validity of the instruments measuring these constructs is sparse. Twelve instruments were identified that may have applicability in measuring organizational constructs in the healthcare setting. The authors describe and characterize these instruments and discuss the implications for nurse administrators

The State of the Science of Health and Wellness for Adults With Intellectual and Developmental Disabilities

Historically, people with intellectual and developmental disabilities (IDD) have experienced health disparities related to several factors including: a lack of access to high quality medical care, inadequate preparation of health care providers to meet their needs, the social determinants of health (e.g., poverty, race and gender), and the failure to include people with IDD in public health efforts and other prevention activities. Over the past decade, a greater effort has been made to both identify and begin to address myriad health disparities experienced by people with IDD through a variety of activities including programs that address health lifestyles and greater attention to the training of health care providers. Gaps in the literature include the lack of intervention trials, replications of successful approaches, and data that allow for better comparisons between people with IDD and without IDD living in the same communities. Implications for future research needed to reduce health disparities for people with IDD include: better monitoring and treatment for chronic conditions common in the general population that are also experienced by people with IDD, an enhanced understanding of how to promote health among those in the IDD population who are aging, addressing the health needs of people with IDD who are not part of the disability service system, developing a better understanding of how to include people with IDD in health and wellness programs, and improving methods for addressing the health care needs of members of this group in an efficient and cost-effective manner, either through better access to general medical care or specialized programs