Let R be a ring and define x ○ y = x + y - xy, which yields a monoid (R, ○), called the circle semigroup of R. This paper investigates the relationship between the ring and its circle semigroup. Of particular interest are the cases
where the semigroup is simple, 0-simple, cancellative, 0-cancellative, regular, inverse, or the union of groups, or where
the ring is simple, regular, or a domain. The idempotents in R coincide with the idempotents in (R, ○) and play an important role in the theory developed.
Prior research has generally established parental attachment as a predictor of problematic Internet use (PIU). However, findings across studies are inconsistent as to which factor(s) of attachment style (i.e., attachment anxiety and attachment avoidance) contributes to PIU. Another gap in the literature is that as most studies highlight the importance of maternal (over paternal) attachment security in inhibiting PIU, little research has examined the possibility of a gender difference, where maternal and paternal attachment securities may exert different influences on males and females.
An anonymous survey was completed by 243 undergraduate students in a public university in the U.S. Midwest. In addition to demographic information, the survey contained measurement scales to assess PIU and parental attachment (both maternal and paternal).
Survey data show that (a) attachment anxiety, but not attachment avoidance, is significantly related to PIU and (b) gender significantly moderates this relationship, where paternal attachment anxiety leads to PIU in female students while maternal attachment anxiety contributes to PIU in male students.
This study deepens our understanding in the relationship between family upbringing, particularly parental attachment, and PIU. More specifically, attachment anxiety is found to be a significant predictor of PIU, but attachment avoidance is not. Also, contributing to the research literature is the finding of a significant gender effect in this relationship.