On a Hereditary Radical Property Relating to the Reducedness

2011 ◽  
Vol 39 (2) ◽  
pp. 608-620 ◽  
Author(s):  
Cheong Mi Ha ◽  
Chan Huh ◽  
Hong Kee Kim ◽  
Nam Kyun Kim ◽  
Yang Lee
Keyword(s):  
Hereditary Radical ◽  
Radical Property

On Rings Whose Strongly Prime Ideals Are Completely Prime

2010 ◽  
Vol 17 (02) ◽  
pp. 283-294 ◽  
Author(s):  
Chan Huh ◽  
Chang Ik Lee ◽  
Yang Lee
Keyword(s):  
Prime Ideals ◽  
Hereditary Radical ◽  
Radical Property

Kaplansky introduced the concept of the K-rings, concerning the commutativity of rings. In this paper, we concentrate on a property of K-rings, introducing the concept of the strongly NI rings, which is stronger than NI-ness. We first examine the relations among the concepts concerned with K-rings and strongly NI rings, constructing necessary examples in the process. We also show that strong NI-ness is a hereditary radical property.

scholarly journals Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings

2008 ◽  
Vol 2008 ◽  
pp. 1-6
Author(s):  
Ravi Srinivasa Rao ◽  
K. Siva Prasad ◽  
T. Srinivas
Keyword(s):  
Jacobson Radical ◽  
Paper Properties ◽  
Hereditary Radical ◽  
Constant Part ◽  
The Right

By a near-ring we mean a right near-ring.J0r, the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radicalJ0rare studied. It is shown thatJ0ris a Kurosh-Amitsur radical (KA-radical) in the variety of all near-ringsR, in which the constant partRcofRis an ideal ofR. So unlike the left Jacobson radicals of types 0 and 1 of near-rings,J0ris a KA-radical in the class of all zero-symmetric near-rings.J0ris nots-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.

scholarly journals On Radical Property of Cross Polyomino Ideal

2019 ◽  
Vol 1306 ◽  
pp. 012023
Author(s):  
Yoshua Yonatan Hamonangan ◽  
Intan Muchtadi-Alamsyah
Keyword(s):  
Radical Property

scholarly journals Representations of constant socle rank for the Kronecker algebra

2020 ◽  
Vol 32 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Daniel Bissinger
Keyword(s):  
Recent Work ◽  
Abelian Groups ◽  
Wild Type ◽  
Kronecker Algebra ◽  
Radical Property

AbstractInspired by recent work of Carlson, Friedlander and Pevtsova concerning modules for p-elementary abelian groups {E_{r}} of rank r over a field of characteristic {p>0}, we introduce the notions of modules with constant d-radical rank and modules with constant d-socle rank for the generalized Kronecker algebra {\mathcal{K}_{r}=k\Gamma_{r}} with {r\geq 2} arrows and {1\leq d\leq r-1}. We study subcategories given by modules with the equal d-radical property and the equal d-socle property. Utilizing the simplification method due to Ringel, we prove that these subcategories in {\operatorname{mod}\mathcal{K}_{r}} are of wild type. Then we use a natural functor {\operatorname{\mathfrak{F}}\colon{\operatorname{mod}\mathcal{K}_{r}}\to% \operatorname{mod}kE_{r}} to transfer our results to {\operatorname{mod}kE_{r}}.

scholarly journals On the mutagenic radical property

1984 ◽  
Vol 27 (3) ◽  
pp. 333-336
Author(s):  
G. Tzintzis
Keyword(s):  
Lower Radical ◽  
Radical Property

In their paper N. Divinsky and A. Sulinski [6] have introduced the notion of mutagenic radical property—that is, a radical property which is far removed from hereditariness—and constructed two such examples. The first is the lower radical property determined by a ring Swo (N. Divinsky [5]) and is an almost subidempotent radical property in the sense of F. Szász [9], and the second is a weakly supernilpotent radical property, that is the lower radical property determined by Swo and all nilpotent rings.

ON BASE RADICAL OPERATORS FOR CLASSES OF FINITE ASSOCIATIVE RINGS

2018 ◽  
Vol 98 (2) ◽  
pp. 239-250 ◽  
Author(s):  
R. G. MCDOUGALL ◽  
L. K. THORNTON
Keyword(s):  
Maximum Order ◽  
Semisimple Class ◽  
Hereditary Radical ◽  
Complete Listing ◽  
Universal Classes ◽  
General Relations ◽  
Associative Rings

In this paper, class operators are used to give a complete listing of distinct base radical and semisimple classes for universal classes of finite associative rings. General relations between operators reveal that the maximum order of the semigroup formed is 46. In this setting, the homomorphically closed semisimple classes are precisely the hereditary radical classes and hence radical–semisimple classes, and the largest homomorphically closed subclass of a semisimple class is a radical–semisimple class.

On homogeneous radicals of semigroup rings of commutative semigroups

1993 ◽  
Vol 123 (5) ◽  
pp. 951-957 ◽  
Author(s):  
A. V. Kelarev
Keyword(s):  
Semigroup Rings ◽  
Commutative Semigroups ◽  
Hereditary Radical

SynopsisAll Archimedean commutative semigroups S are described such that every S-homogeneous hereditary radical is S-normal. It is shown that this result is in a sense unimprovable.

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