r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

BACKGROUND Studies assessing active commuting to school usually use simple questionnaires, and often is mode of commuting reported with a single questionnaire item only. The purpose of the present study is to report the test-retest reliability of a newly developed comprehensive questionnaire on active commuting to school and work among 6th grade school children and their parents in Norway. ME...

AIM The purpose of the present study is to examine the prevalence of active commuting and factors associated with participation in active commuting in the municipality of Karlskrona, Sweden. Active commuting is defined here as walking or cycling to and from school/work for at least 15 minutes one-way. METHOD A cross-sectional study was carried out, which included baseline data from parents-to...

Matrices that are products of two (or more) commuting square-zero matrices and matrices that are products of two commuting nilpotent matrices are characterized. Also given are characterizations of operators on an infinite dimensional Hilbert space that are products of two (or more) commuting square-zero operators, as well as operators on an infinite-dimensional vector space that are products of...

In this note, we show that the set of all commuting d-tuples of commuting n × n matrices that are contained is an n-dimensional commutative algebra is a closed set, and therefore, Gerstenhaber’s theorem on commuting pairs of matrices is a consequence of the irreducibility of the variety of commuting pairs. We show that the variety of commuting triples of 4×4 matrices is irreducible. We also stu...

BACKGROUND Few studies have assessed the predictors of changes in commuting. This study investigated the associations between physical environmental characteristics and changes in active commuting. METHODS Adults from the population-based European Prospective Investigation into Cancer (EPIC)-Norfolk cohort self-reported commuting patterns in 2000 and 2007. Active commuters were defined as tho...

INTRODUCTION Active commuting is associated with a reduced risk of several chronic diseases, but few studies have considered institutional factors that influence it. We examined the association between cultural and physical workplace supports for active commuting and employee active commuting behavior. METHODS Data were collected from employees (N = 375) in Manhattan, Kansas, via an online su...

BACKGROUND The current study examined the associations between active commuting to school, cognitive performance, and academic achievement in Dutch adolescents. In addition, it was explored whether these associations were moderated by sex and mediated by depressive symptoms. METHODS Students in grades 7 and 9 (N = 270; mean age 13.4 years; 53% boys) were included. Active commuting to school w...