scholarly journals Primeradicals in Ternary Semi Groups

2019 ◽  
Vol 8 (6S4) ◽  
pp. 1402-1404
Keyword(s):  
Prime Radical ◽  
Radical Ideal

In this paper we study the properties of prime radical of an ideal in a ternarysemigroup. We characterize different classes of ternarysemigroups by their properties of their radicals and nilpotent. We introduced and charaterize the notions of radical ideal generated by P in ternarysemigroups.

ON EXTENSION OF PRIME RADICAL IN 2-PRIMAL NEAR-RINGS

2020 ◽  
Vol 9 (3) ◽  
pp. 1339-1348
Author(s):  
B. Elavarasan ◽  
K. Porselvi and J. Catherine Grace John ◽  
Porselvi J. Catherine Grace John
Keyword(s):  
Prime Radical

On the prime radical of a module over a commutative ring

1992 ◽  
Vol 20 (12) ◽  
pp. 3593-3602 ◽  
Author(s):  
James Jenkins ◽  
Patrick F. Smith
Keyword(s):  
Commutative Ring ◽  
Prime Radical

ON THE GROENEWALD-HEYMAN STRONGLY PRIME RADICAL

1984 ◽  
Vol 7 (3) ◽  
pp. 225-240 ◽  
Author(s):  
M. M. Parmenter ◽  
P. N. Stewart ◽  
R. Wiegandt
Keyword(s):  
Prime Radical

scholarly journals On the Prime Radical of a Hypergroupoid

2005 ◽  
Vol 1 (3) ◽  
pp. 234-238 ◽  
Author(s):  
Gursel Yesilot
Keyword(s):  
Prime Radical

A GENERALIZATION OF BAER'S LOWER NILRADICAL FOR MODULES

2007 ◽  
Vol 06 (02) ◽  
pp. 337-353 ◽  
Author(s):  
MAHMOOD BEHBOODI
Keyword(s):  
Prime Ring ◽  
Artinian Ring ◽  
Prime Radical ◽  
Nilpotent Elements ◽  
Noetherian Domain ◽  
Prime Submodules ◽  
Strongly Nilpotent ◽  
Commutative Domain ◽  
Torsion Modules

Let M be a left R-module. A proper submodule P of M is called classical prime if for all ideals [Formula: see text] and for all submodules N ⊆ M, [Formula: see text] implies that [Formula: see text] or [Formula: see text]. We generalize the Baer–McCoy radical (or classical prime radical) for a module [denoted by cl.rad R(M)] and Baer's lower nilradical for a module [denoted by Nil *(RM)]. For a module RM, cl.rad R(M) is defined to be the intersection of all classical prime submodules of M and Nil *(RM) is defined to be the set of all strongly nilpotent elements of M (defined later). It is shown that, for any projective R-module M, cl.rad R(M) = Nil *(RM) and, for any module M over a left Artinian ring R, cl.rad R(M) = Nil *(RM) = Rad (M) = Jac (R)M. In particular, if R is a commutative Noetherian domain with dim (R) ≤ 1, then for any module M, we have cl.rad R(M) = Nil *(RM). We show that over a left bounded prime left Goldie ring, the study of Baer–McCoy radicals of general modules reduces to that of torsion modules. Moreover, over an FBN prime ring R with dim (R) ≤ 1 (or over a commutative domain R with dim (R) ≤ 1), every semiprime submodule of any module is an intersection of classical prime submodules.

Radicals in differential polynomial rings

2020 ◽  
pp. 1-17
Author(s):  
Jongwook Baeck ◽  
Nam Kyun Kim ◽  
Yang Lee
Keyword(s):  
Differential Polynomial ◽  
Prime Radical ◽  
Polynomial Rings

In this paper, we present new characterizations of several radicals of differential polynomial rings, including the Levitzki radical, strongly prime radical, and uniformly strongly prime radical in terms of the related [Formula: see text]-radical.

On the f-Prime Radical of Near-Rings

2005 ◽  
pp. 293-299
Author(s):  
Satyanarayana Bhavanari ◽  
Richard Wiegandtt
Keyword(s):  
Prime Radical

scholarly journals On the closure of the prime radical of a Banach algebra

1993 ◽  
Vol 36 (3) ◽  
pp. 421-425 ◽  
Author(s):  
D. W. B. Somerset ◽  
G. A. Willis
Keyword(s):  
Banach Algebra ◽  
Prime Radical ◽  
Prime Ideals ◽  
The Relationship

The relationship between the prime ideals and the primal ideals of a Banach algebra is investigated. It is shown that the closure of the prime radical of a Banach algebra may be properly contained in the intersection of the closed primal ideals of the algebra.

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