Linkage of modules over Cohen-Macaulay rings

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new condition and other module-theory conditions such as G-dimension and sequentially Cohen-Macaulay are established. By the way several already known theorems in linkage theory are improved or recovered by new approaches.Comment: 12 Page

Investigating the factors affecting the development of the humanitarian aid supply chain by popular athletes

The present study was designed and conducted to investigate the factors affecting the development of the humanitarian aid supply chain by popular athletes. The present study is one of the mixed researches which were done in the form of qualitative and quantitative methods. The statistical population of the present study in the qualitative section includes elites and experts in the field of the humanitarian supply chain, sports sociology, sports management, and crisis management. According to the purposeful selection, 13 people were identified as the research sample. In the quantitative part of the present study, in addition to the elites in the field of the humanitarian supply chain, sports sociology, sports management, and crisis management, some experts of the Crisis Management Organization and popular athletes were added to the statistical community. The collection tools of the present study included a semi-structured interview and a researcher-made questionnaire. In the quantitative analysis of the research, the structural equation method with the PLS approach has been used. The results of the present study showed that; 25 micro actives were extracted through interviews, these factors were divided into 5 categories: cultural, managerial, legal, human, and communication-technological factors. The research results showed that; among the factors affecting the development of the humanitarian aid supply chain through popular athletes, managerial factors had the most role and importance (impact = 0.983; T-factor = 427.756). This highlights the importance and necessity of management platforms for the development of the humanitarian aid supply chain through popular athletes

The homotopy Lie algebra of a Tor-independent tensor product

In this article we investigate a pair of surjective local ring maps $S_1\leftarrow R\to S_2$ and their relation to the canonical projection $R\to S_1\otimes_R S_2$, where $S_1,S_2$ are Tor-independent over $R$. Our main result asserts a structural connection between the homotopy Lie algebra of $S:=S_1\otimes_R S_2$, denoted $\pi(S)$, in terms of those of $R,S_1$ and $S_2$. Namely, $\pi(S)$ is the pullback of (adjusted) Lie algebras along the maps $\pi(S_i)\to \pi(R)$ in various cases, including when the maps above have residual characteristic zero. Consequences to the main theorem include structural results on Andr\'{e}-Quillen cohomology, stable cohomology, and Tor algebras, as well as an equality relating the Poincar\'{e} series of the common residue field of $R,S_1,S_2$ and $S$.Comment: 20 pages. Corrected a mistake in 1.7; simplified and reorganized Sections 4 and