Abstract. We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In section 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.

The Affordable Care Act of 2010 launch of Medicare Value-Based Purchasing has become the platform for payment reform. It is a mechanism by which buyers of health care services hold providers accountable for high-quality and cost-effective care. The objective of the study was to examine the relationship between quality of hospital care and hospital competition using the quality-quantity behavioral model of hospital behavior. The quality-quantity behavioral model of hospital behavior was used as the conceptual framework for this study. Data from the American Hospital Association database, the Hospital Compare database, and the Area Health Resources Files database were used. Multivariate regression analysis was used to examine the effect of hospital competition on patient mortality. Hospital market competition was significantly and negatively related to the 3 mortality rates. Consistent with the literature, hospitals located in more competitive markets had lower mortality rates for patients with acute myocardial infarction, heart failure, and pneumonia. The results suggest that hospitals may be more readily to compete on quality of care and patient outcomes. The findings are important because policies that seek to control and negatively influence a competitive hospital environment, such as Certificate of Need legislation, may negatively affect patient mortality rates. Therefore, policymakers should encourage the development of policies that facilitate a more competitive and transparent health care marketplace to potentially and significantly improve patient mortality.

We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In section 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.

Abstract. We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In section 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.