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ISPC Materials and technologies, Philadelphia, USA 

* Scientific Article * Impact Factor 6.630 

Mushrub VA, Sukhorukova IV, Mochalina EP, Ivankova GV
SOME PROPERTIES OF THE LATTICE OF FCLOSED RIGHT IDEALS. 


Full Article: PDF
Scientific Object Identifier: http://soi.org/1.1/TAS075117
DOI: https://dx.doi.org/10.15863/TAS.2017.07.51.17
Language: English
Citation: Mushrub VA, Sukhorukova IV, Mochalina EP, Ivankova GV (2017) SOME PROPERTIES OF THE LATTICE OF FCLOSED RIGHT IDEALS. ISJ Theoretical & Applied Science, 07 (51): 103106. Soi: http://soi.org/1.1/TAS075117 Doi: https://dx.doi.org/10.15863/TAS.2017.07.51.17 
Pages: 103106
Published: 30.07.2017
Abstract: Throughout this paper R is a unitary associative ring and f is an injective ring endomorphiosm of R. In the present article, we introduce the notion of the lattice Lat(R, f ) of all fclosed right ideals of R with some special operation instead of the intersection operation. The paper is devoted to the study of this lattice. In particular, we investigate the interrelationship between the lattice of all fclosed right ideals of R and the lattice of right ideals of the CohnJordan extension A. We obtained some results in this direction. In Theorem 1 we give necessary and sufficient conditions, in terms of the lattice Lat(R, f ), for the CohnJordan extension A be a right Artinian ring. This theorem implies in particular that A is right Artinian provided that R is right Artinian. Theorem 2 is a structural theorem and states that a ring R with a bounded length of chains of the right fclosed ideals is embeddable in a semisimple Artinian ring. The authors’ original proof is based on the CohnJordan extension. The CohnJordan extensions were first introduced in [8] for the study of skew polynomial rings constructed by means of a ring endomorphism. Five open questions are formulated.
Key words: lattice, composition length, right Artinian rings

