A Homological Approach to Factorization

Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated localizations of D and projections onto partially ordered quotient groups of G(D). We use this functor to construct many cochain complexes of o-homomorphisms of po-groups. These complexes naturally lead to some fundamental structure theorems and some natural homology theory that provide insight into the factorization behavior of D.Comment: Submitted for publication 12/15/201

Player Preferences for Coaching Behaviors

In athletics every athlete prefers different behaviors from their coach. Research hasn’t been able to explain player preferences in terms of their preferred and expected coaching behaviors and if their coaches are meeting those behaviors. This study looked to see if coaches met the expected and preferred behaviors of their athletes. In order to examine this question, St. John Fisher student athletes of both genders, and individual sport and team sport athletes were be surveyed. After examining prior research, results are expected to show that athletes prefer coaches who are inclusive in decision making, focus on building skills, and develop a positive coach-athlete relationship. Of the 581 student athletes at St. John Fisher College, 87 responded to the survey. The results revealed that athletes preferred a coach to work on improving their skills and building a relationship with them in season, and a coach who does not make all the decisions by himself. There was no significant difference in the expectations and preferences between males and females, type of sport, and the year of the athlete

Exciting Changes in the Way Curriculum is Proposed and Approved

New processes, tools, and priorities will make this a year of change for faculty as they design or modify courses and programs. Come have a conversation with the Curriculum & Gen Ed Committees to better understand how these changes will impact you and your programs. This program is especially important for those planning to propose new or significantly modified program changes for the 2020–21 catalog

On the integral closure of a half-factorial domain

AbstractA half-factorial domain (HFD), R, is an atomic integral domain where given any two products of irreducible elements of R:α1α2⋯αn=β1β2⋯βmthen n=m.As a natural generalization of unique factorization domains (UFD), one wishes to investigate which “good” properties of UFDs that HFDs possess. In particular, it has been conjectured that the integral closure of a half-factorial domain is again a HFD (see Non-Noetherian Commutative Ring Theory, Mathematics and its applications, Vol. 520, Kluwer, Dordrecht, 2000, pp. 97–115. for example). In this paper we produce an example that demonstrates that the integral closure of a HFD does not even have to be atomic. We shall investigate the failure of this conjecture closely and highlight some cases where the conjecture does indeed hold

Elasticity Properties Preserved in the Normset

AbstractLet T⊆R be the rings of integers in a number field and a finite Galois extension field. We study relations between the elasticity ρ(R) of the monoid of nonzero elements of R and the elasticity ρ(S) of the monoid S of norms to T of those elements. We show ρ(R)⩾ρ(S) and that equality holds if the norms of irreducible elements of R are irreducible in S, which is true, in particular, if either ρ(R)<2 or ρ(S)=1

Exploring the Impacts of COVID-19 on LGBTQ+ Intimate Communication

The question guiding this exploratory qualitative research study is, “How has the COVID-19 pandemic impacted LGBTQ+ intimate communication and relationships?” Recently, scholars have demanded that communication scholarship be conducted through an intersectional lens that analyzes multiple dimensions of social identities, including LGBTQ+ identities. Queer Theory poses questions around gender, sexual, and romantic identities that can help expand our understanding of different forms of intimate communication. “Queering” interpersonal communication research involves challenging traditional understandings of communication within identities such as sexuality and gender at the individual and structural levels (Chevrette, 2013). Queering communication research supports a more in depth analysis of how identities influence the ways we communicate with others and build interpersonal relationships (Elia, 2003). An additional aspect to this research involves the highly contagious nature of the COVID-19 virus, which has drastically transformed how individuals socialize and has largely been unexplored within the communication discipline. This research project not only expands our understanding of how the COVID-19 pandemic has impacted LGBTQ+ intimate relationships and communication, but also proves valuable to Queering interpersonal communication scholarship. Data were collected through semi-structured one-on-one interviews with LGBTQ+ identified individuals in order to explore how the COVID-19 pandemic has impacted their intimate communication and relationships. Interviews were transcribed and coded thematically and inductively. The transcriptions were analyzed through an interpretive narrative approach to highlight individual lived experiences of LGBTQ+ community members. Findings reflect the particular ways in which members of the LGBTQ+ community have been impacted by social isolation and developed resilience during the COVID-19 pandemic by maintaining relationships and a sense of community through digital communication

Perceptions of Illinois Community College Chief Academic Officers: Fulfilling the Mission

This study documents voices of the most experienced active Illinois community college chief academic officers (CAOs). Adaptive leadership theory is used to frame the effort of CAOs to infuse accountability into the core community college open access mission. The analysis of conversations with these CAOs reveals a focus on accountability that centers around student success initiatives rather than an urgent need to improve completion rate. The CAOs interviewed perceived student success and open access as crucial components of the mission of community colleges. The CAOs describe the work they do to help fulfill the mission and how that work has changed during the COVID-19 pandemic. Advice is provided for those who aspire to the CAO position and for those responsible for developing future CAOs