Let M be a lattice module over the multiplicative lattice L. A nonzero L-lattice module M is called second if for each a ∈ L, a1M = 1M or a1M = 0M . A nonzero L-lattice module M is called secondary if for each a ∈ L, a1M = 1M or a(n)1M = 0 M for some n > 0. Our objective is to investigative properties of second and secondary lattice modules.

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.

Low tracking accuracy of trackers, structure vibration by winds, and lens deformation temperature lead to non-vertical incident irradiation Fresnel lens, which necessitates a secondary concentrator in actual engineering application concentrating photovoltaic module. In this study, focusable uniform convergence microprism is added between solar cell improve efficiency focal spot energy uniformit...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

1 Department of Computer Science and Engineering, Arizona State University, Tempe, Arizona 85287-5406, [email protected] Abstract -This paper describes a project underway at Arizona State University to develop an innovative secondary school software development curriculum module which provides students with a better understanding of the software development field, dispels misconceptions and, h...

The study was aimed at designing and developing a Physics module based on learning style and appropriate technology in secondary educational setting by employing Isman Instructional Design Model and to test the effectiveness of the module. The paper draws attention to the design principles which employs Isman Instructional Design Model. The prototype module was tested among two teachers and 14 ...