scholarly journals The image of Jordan left derivations on algebras

2019 ◽  
Vol 38 (6) ◽  
pp. 53-61
Author(s):  
Amin Hosseini ◽  
Ajda Fosner
Keyword(s):  
Semiprime Ideal ◽  
Left Derivation

Let A be an algebra, and let I be a semiprime ideal of A. Suppose thatd : A → A is a Jordan left derivation such that d(I) ⊆ I.We prove that if dim{d(a)+I : a ⋲ A} ≤ 1, then d(A) ⊆ I. Additionally, we consider several consequences of this result.

ON THE SEMIPRIME IDEAL LATTICE OF A RIGHT INVARIANT RING

1991 ◽  
Vol 14 (3) ◽  
pp. 255-260
Author(s):  
J. G. Raftery ◽  
T. Sturm
Keyword(s):  
Ideal Lattice ◽  
Semiprime Ideal ◽  
Invariant Ring

Factoring Ideals into Semiprime Ideals

1978 ◽  
Vol 30 (6) ◽  
pp. 1313-1318 ◽  
Author(s):  
N. H. Vaughan ◽  
R. W. Yeagy
Keyword(s):  
Integral Domain ◽  
Dedekind Domain ◽  
Prime Ideals ◽  
Semiprime Ideal ◽  
Dedekind Domains

Let D be an integral domain with 1 ≠ 0 . We consider “property SP” in D, which is that every ideal is a product of semiprime ideals. (A semiprime ideal is equal to its radical.) It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals. We prove that a domain D with property SP is almost Dedekind, and we give an example of a nonnoetherian almost Dedekind domain with property SP.

scholarly journals L-Fuzzy Semiprime Ideals of a Poset

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Berhanu Assaye Alaba ◽  
Derso Abeje Engidaw
Keyword(s):  
Prime Ideal ◽  
Prime Ideals ◽  
Semiprime Ideal

In this paper, we introduce the concept of L-fuzzy semiprime ideal in a general poset. Characterizations of L-fuzzy semiprime ideals in posets as well as characterizations of an L-fuzzy semiprime ideal to be L-fuzzy prime ideal are obtained. Also, L-fuzzy prime ideals in a poset are characterized.

scholarly journals A note on Cohn's universal localisation at a semiprime ideal

2004 ◽  
Vol 69 (3) ◽  
pp. 361-367
Author(s):  
John A. Beachy
Keyword(s):  
Noetherian Ring ◽  
Injective Envelope ◽  
Semiprime Ideal

The universal localisation RΓ(s) at a semiprime ideal S of a left Noetherian ring R was defined and studied by P. M. Cohn. In this note we investigate the interaction between the universal localisation RΓ(s), the Ore localisation at S, and the torsion-theoretic localisation at the injective envelope E(R/S) of the module R(R/S).

Localization at a semiprime ideal of a right noetherian ring

1977 ◽  
Vol 5 (7) ◽  
pp. 707-726 ◽  
Author(s):  
J.H. Cozzens ◽  
F.L. Sandomierski
Keyword(s):  
Noetherian Ring ◽  
Semiprime Ideal

scholarly journals On Generalized Derivations ofBCI-Algebras and Their Properties

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
L. Kamali Ardekani ◽  
B. Davvaz
Keyword(s):  
Generalized Derivations ◽  
Fundamental Properties ◽  
Left Derivation

We introduce the concept of(f,g)-derivations ofBCI-algebras and we investigate some fundamental properties and establish some results on(f,g)-derivations. Also, we treat to generalization of right derivation and left derivation ofBCI-algebras and consider some related properties.

scholarly journals COMPLEMENT OF THE ZERO DIVISOR GRAPH OF A LATTICE

2013 ◽  
Vol 89 (2) ◽  
pp. 177-190 ◽  
Author(s):  
VINAYAK JOSHI ◽  
ANAGHA KHISTE
Keyword(s):  
Zero Divisor ◽  
Semiprime Ideal ◽  
Zero Divisor Graph

AbstractIn this paper, we determine when $\mathop{({\Gamma }_{I} (L))}\nolimits ^{c} $, the complement of the zero divisor graph ${\Gamma }_{I} (L)$ with respect to a semiprime ideal $I$ of a lattice $L$, is connected and also determine its diameter, radius, centre and girth. Further, a form of Beck’s conjecture is proved for ${\Gamma }_{I} (L)$ when $\omega (\mathop{({\Gamma }_{I} (L))}\nolimits ^{c} )\lt \infty $.

scholarly journals Jordan left (?,?) -derivations Of ?-prime rings

2011 ◽  
Vol 8 (3) ◽  
pp. 826-831
Author(s):  
Baghdad Science Journal
Keyword(s):  
Prime Rings ◽  
Left Derivation

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.

Sign in / Sign up

Export Citation Format

Share Document