A New Criterion for Embeddability in a Zero‐Dimensional Commutative Ring

Author(s):  
Robert Gilmer
2019 ◽  
Vol 56 (2) ◽  
pp. 252-259
Author(s):  
Ebrahim Hashemi ◽  
Fatemeh Shokuhifar ◽  
Abdollah Alhevaz

Abstract The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R0[x] equals to the set of all nilpotent elements of R0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R0[x] is a subset of the intersection of all maximal left ideals of R0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R0[x] coincides with the intersection of all maximal left ideals of R0[x]. Moreover, we prove that the quasi-radical of R0[x] is the greatest quasi-regular (right) ideal of it.


2019 ◽  
Vol 29 (6) ◽  
pp. 215-228

This paper deals with the impact that Karl Marx"s Das Kapital (and especially its fourth volume, the theory of Surplus Value) had on the category of economy in Kazimir Malevich"s output. In a series of texts, Malevich proclaims economy the new criterion of art and the Black Square its embodiment in contemporary painting. While the author was analyzing Marx"s views on labor and human nature, echoes of them turned up in Malevich"s manifestos and philosophical essays where the artist pondered the idea of the liberation of creative exaltation. The article others an interpretation of the creative process itself from the standpoint of economy, which for Malevich provided an opportunity to lay down the foundation for a new kind of art that was consistent with the prevailing ideology. The author points out that while Malevich was in Vitebsk he studied Marx"s works with idea of incorporating economic studies into art: his speculations on the relationships between the ideological superstructure and the practical, economic base were written in the manner of Marxist philosophy and provided the basis for his main essays, The World as Non-Objectivity (1923) and Suprematism: Thee World as Non-Objectivity or Eternal Rest (1923-1924). They defined the new art as an independent ideological superstructure positioned “outside of other contents and ideologies.” Parallel to that, the author examines the correspondence between Malevich"s theory of the surplus element and Marxist doctrines on surplus value. It is also shown that Malevich hoped to prove that, as in dialectical materialism, his new surplus element opens the way to a new artistic structure that is emerging from the womb of the old system in the same way that communism comes about as a kind of heterogeneous body from within the underpinnings of bourgeois society.


Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2933-2941 ◽  
Author(s):  
Unsal Tekir ◽  
Suat Koc ◽  
Kursat Oral

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ? I with a ? ?0, then b ? I for every a,b ? R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.


2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.


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