All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. ...

In automated synthesis, given a specification, we automatically create a system that is guaranteed to satisfy the specification. In the classical temporal synthesis algorithms, one usually creates a “flat” system “from scratch”. However, real-life software and hardware systems are usually created using preexisting libraries of reusable components, and are not “flat” since repeated sub-systems a...

In automated synthesis, given a specification, we automatically create a system that is guaranteed to satisfy the specification. In the classical temporal synthesis algorithms, one usually creates a “flat” system “from scratch”. However, real-life software and hardware systems are usually created using preexisting libraries of reusable components, and are not “flat” since repeated subsystems ar...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

Microfiltration can clarify pomegranate juice; however, fouling is a limiting phenomenon in the process. In current work ultrasound was applied above and below the membrane surface to reduce fouling after removing temperature effect. A hydrophilic mixed cellulose ester membrane with pore size of 0.45 μm was used in lab scale flat sheet module. Membrane module was placed above and below the ultr...

Microfiltration can clarify pomegranate juice; however, fouling is a limiting phenomenon in the process. In current work ultrasound was applied above and below the membrane surface to reduce fouling after removing temperature effect. A hydrophilic mixed cellulose ester membrane with pore size of 0.45 μm was used in lab scale flat sheet module. Membrane module was placed above and below the ultr...

Recently two different concepts of covers of acts over monoids have been studied by a number of authors and many interesting results discovered. One of these concepts is based on coessential epimorphisms and the other is based on Enochs’ definition of a flat cover of a module over a ring. Two recent papers have suggested that in the former case, strongly flat covers are not unique. We show that...

In this document we illustrate the module preservation statistics on simulated data. We describe the simulation method and seven simulation studies in more detail than in the main text. The design and main results of the simulations are summarized in Figure 8 of the main article which we reproduce here for convenience in Figure 1. A complete table of results can be found in the accompanying Sup...

Carbon molecular sieve membranes (CMSMs) have been considered as very promising candidates for gas separation, in terms of separation properties as well as thermal and chemical stability. Due to the numerous advantages and wide applications of carbon membranes, their application for gas separation is of special importance. Because of the importance of carbon membranes and a large number of stud...