A note on almost prime submodule of CSM module over principal ideal domain

An almost prime submodule is a generalization of prime submodule introduced in 2011 by Khashan. This algebraic structure was brought from an algebraic structure in ring theory, prime ideal, and almost prime ideal. This paper aims to construct similar properties of prime ideal and almost prime ideal from ring theory to module theory. The problem that we want to eliminate is the multiplication operation, which is missing in module theory. We use the definition of module annihilator to bridge the gap. This article gives some properties of the prime submodule and almost prime submodule of CMS module over a principal ideal domain. A CSM module is a module that every cyclic submodule. One of the results is that the idempotent submodule is an almost prime submodule.

N Sequence Prime Ideals

In this paper, the concepts of -sequence prime ideal and -sequence quasi prime ideal are introduced. Some properties of such ideals are investigated. The relations between -sequence prime ideal and each of primary ideal, -prime ideal, quasi prime ideal, strongly irreducible ideal, and closed ideal, are studied. Also, the ideals of a principal ideal domain are classified into quasi prime ideals and -sequence quasi prime ideals.

Feel the music : crossmodal integration in music perception

n addition to auditory information, music perception often involves visual and vibrotactile information, making it an ideal domain through which to study cross-modal integration. Recent research has demonstrated a strong influence of visual information on auditory judgments concerning music. However, we have very little empirical information regarding integration of vibrotactile information in music. In Experiment 1, participants made judgments of interval size for unimodal presentations of melodic intervals in auditory, visual, and vibrotactile conditions. In Experiment 2, participants made judgments of interval size for cross-modal presentations of intervals comprised of stimuli presented in the three unimodal conditions of Experiment 1. In Experiment 3, participants were trained with vibrotactile stimuli to assess if learning benefits audio-vibrotactile integration in music perception. The results are discussed in light of differences in the extent of visual and vibrotactile influence on auditory judgments and the role of learning in cross-modal integration in music.

Feel the music : crossmodal integration in music perception

n addition to auditory information, music perception often involves visual and vibrotactile information, making it an ideal domain through which to study cross-modal integration. Recent research has demonstrated a strong influence of visual information on auditory judgments concerning music. However, we have very little empirical information regarding integration of vibrotactile information in music. In Experiment 1, participants made judgments of interval size for unimodal presentations of melodic intervals in auditory, visual, and vibrotactile conditions. In Experiment 2, participants made judgments of interval size for cross-modal presentations of intervals comprised of stimuli presented in the three unimodal conditions of Experiment 1. In Experiment 3, participants were trained with vibrotactile stimuli to assess if learning benefits audio-vibrotactile integration in music perception. The results are discussed in light of differences in the extent of visual and vibrotactile influence on auditory judgments and the role of learning in cross-modal integration in music.

Exploring the Beginnings of Algebraic K-Theory

According to Atiyah, K-theory is that part of linear algebra that studies additive or abelian properties (e.g. the determinant). Because linear algebra, and its extensions to linear analysis, is ubiquitous in mathematics, K-theory has turned out to be useful and relevant in most branches of mathematics. Let R be a ring. One defines K0(R) as the free abelian group whose basis are the finitely generated projective R-modules with the added relation P ⊕ Q = P + Q. The purpose of this thesis is to study simple settings of the K-theory for rings and to provide a sequence of examples of rings where the associated K-groups K0(R) get progressively more complicated. We start with R being a field or a principle ideal domain and end with R being a polynomial ring on two variables over a non-commutative division ring.

On Graded 2-Prime Ideals

The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different. Furthermore, we show that graded 2-prime ideals and graded weakly prime ideals are also different. Several properties of graded 2-prime ideals are investigated. We study graded rings in which every graded 2-prime ideal is graded prime, we call such a graded ring a graded 2-P-ring. Moreover, we introduce the concept of graded semi-primary ideals, and show that graded 2-prime ideals and graded semi-primary ideals are different concepts. In fact, we show that graded semi-primary, graded 2-prime and graded primary ideals are equivalent over Z-graded principal ideal domain.

Strongly D2 modules and their applications

An [Formula: see text]-module [Formula: see text] is called strongly [Formula: see text] if [Formula: see text] is a [Formula: see text] (equivalently, direct projective) module for every positive integer [Formula: see text]. In this paper, we consider the class of quasi-projective [Formula: see text]-modules, the class of strongly [Formula: see text] [Formula: see text]-modules and the class of [Formula: see text]-modules. We first show that these classes are distinct, which gives a negative answer to the question raised by Li–Chen–Kourki. We also give structural characterizations of strongly [Formula: see text] modules for finitely generated modules over a principal ideal domain. In addition, we characterize some rings such as Artinian semisimple rings, hereditary rings, semihereditary rings and perfect rings in terms of strongly [Formula: see text] modules.

Design of Smart Greenhouse for Environmental Engineering using Internet of Things

A nursery means to give ideal light and shield plants from the antagonistic atmosphere which conveys an ideal domain for plant development. A keen nursery is worked with capacity in condition control. The brilliant gadget is introduced in the nursery comprises of numerous sensors, which estimates condition boundaries, for example, temperature and air dampness. One of the ecological key boundaries is temperature. The gadget utilizes this boundary to give legitimate temperature to plant development. The deliberate information is sent to the information worker by using the Message Queuing Telemetry Transport convention through the Internet of Things design. The shrewd gadget has prevailing with regards to estimating boundaries and performed natural building. The temperature and air moistness sensors have normal blunder estimations.

On solvability of the matrix equation AXB = C over a principal ideal domain

In this paper we present conditions of solvability of the matrix equation AXB = B over a principal ideal domain. The necessary and sufficient conditions of solvability of equation AXB = B in term of the Smith normal forms and in term of the Hermi-te normal forms of matrices constructed in a certain way by using the coefficients of this equation are proposed. If a solution of this equation exists we propose the method for its construction.