scholarly journals Generalized Higher Derivations on ΓM-Modules

2020 ◽  
pp. 35-44
Author(s):  
Auday Hekmat Mahmood ◽  
Mahdi Saleh Nayef ◽  
Salah Mehdi Salih
Keyword(s):  
Higher Derivation ◽  
Torsion Free

The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓM-modules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c M and α,βΓ, is Jordan generalized triple higher derivation of M into X.

scholarly journals Jordan higher derivations in prime ?-rings

2016 ◽  
Vol 27 (2) ◽  
pp. 155-163
Author(s):  
MM Rahman ◽  
AC Paul
Keyword(s):  
Prime Ring ◽  
Prime Rings ◽  
Higher Derivation ◽  
Torsion Free

The objective of this paper is to study Jordan higher derivations in prime ? -rings. We introduce a higher derivation and a Jordan higher derivation in ? -rings. For a 2-torsion free prime ? -ring M which satisfies the condition a?b?c = a?b?c for all a,b, c?M and ? ,? ?? , we prove that every Jordan higher derivation D = (di)i?N0 of M is a higher derivation of M Bangladesh J. Sci. Res. 27(2): 155-163, December-2014

LIE -HIGHER DERIVATIONS AND LIE -HIGHER DERIVABLE MAPPINGS

2017 ◽  
Vol 96 (2) ◽  
pp. 223-232
Author(s):  
YANA DING ◽  
JIANKUI LI
Keyword(s):  
Commutative Ring ◽  
Free Algebra ◽  
Linear Mapping ◽  
Higher Derivation ◽  
Formula Derivation ◽  
Transfer Problems ◽  
Torsion Free

Let ${\mathcal{A}}$ be a unital torsion-free algebra over a unital commutative ring ${\mathcal{R}}$. To characterise Lie $n$-higher derivations on ${\mathcal{A}}$, we give an identity which enables us to transfer problems related to Lie $n$-higher derivations into the same problems concerning Lie $n$-derivations. We prove that: (1) if every Lie $n$-derivation on ${\mathcal{A}}$ is standard, then so is every Lie $n$-higher derivation on ${\mathcal{A}}$; (2) if every linear mapping Lie $n$-derivable at several points is a Lie $n$-derivation, then so is every sequence $\{d_{m}\}$ of linear mappings Lie $n$-higher derivable at these points; (3) if every linear mapping Lie $n$-derivable at several points is a sum of a derivation and a linear mapping vanishing on all $(n-1)$th commutators of these points, then every sequence $\{d_{m}\}$ of linear mappings Lie $n$-higher derivable at these points is a sum of a higher derivation and a sequence of linear mappings vanishing on all $(n-1)$th commutators of these points. We also give several applications of these results.

Jordan k-Homomorphisms onto Completely Prime ΓN Rings

1970 ◽  
Vol 30 ◽  
pp. 32-40
Author(s):  
Sujoy Charaborty ◽  
Akhil Chandra Paul
Keyword(s):  
Torsion Free

By introducing the notions of k-homomorphism, anti-k-homomorphism and Jordan khomomorphism of Nobusawa Γ -rings, we establish some significant results related to these concepts. If M1 is a Nobusawa Γ1 -ring and M2 is a 2-torsion free completely prime Nobusawa Γ2 -ring, then we prove that every Jordan k-homomorphism θ of M1 onto M2 such that k(Γ1 ) = Γ2 is either a k-homomorphism or an anti-k-homomorphism. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 32-40 DOI: http://dx.doi.org/10.3329/ganit.v30i0.8500  

Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

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.

New definition of MV-semimodules

2021 ◽  
pp. 1-12
Author(s):  
Simin Saidi Goraghani ◽  
Rajab Ali Borzooei ◽  
Sun Shin Ahn
Keyword(s):  
Basic Properties ◽  
Mv Algebra ◽  
Definition Of ◽  
Torsion Free

In recent years, A. Di Nola et al. studied the notions of MV-semiring and semimodules and investigated related results [9, 10, 12, 26]. Now in this paper, by using an MV-semiring and an MV-algebra, we introduce the new definition of MV-semimodule, study basic properties and find some examples. Then we study A-ideals on MV-semimodules and Q-ideals on MV-semirings, and by using them, we study the quotient structures of MV-semimodule. Finally, we present the notions of prime A-ideal, torsion free MV-semimodule and annihilator on MV-semimodule and we study the relations among them.

On the square subgroups of decomposable torsion-free abelian groups of rank three

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Fysal Hasani ◽  
Fatemeh Karimi ◽  
Alireza Najafizadeh ◽  
Yousef Sadeghi
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Free Abelian Groups ◽  
Torsion Free

AbstractThe square subgroup of an abelian group

scholarly journals Self-splitting Abelian groups

2001 ◽  
Vol 64 (1) ◽  
pp. 71-79 ◽  
Author(s):  
P. Schultz
Keyword(s):  
Abelian Group ◽  
Direct Product ◽  
Free Module ◽  
Research Report ◽  
Original Form ◽  
Original Research ◽  
Direct Sum ◽  
The University ◽  
Torsion Free ◽  
Made In

G is reduced torsion-free A belian group such that for every direct sum ⊕G of copies of G, Ext(⊕G, ⊕G) = 0 if and only if G is a free module over a rank 1 ring. For every direct product ΠG of copies of G, Ext(ΠG,ΠG) = 0 if and only if G is cotorsion.This paper began as a Research Report of the Department of Mathematics of the University of Western Australia in 1988, and circulated among members of the Abelian group community. However, it was never submitted for publication. The results have been cited, widely, and since copies of the original research report are no longer available, the paper is presented here in its original form in Sections 1 to 5. In Section 6, I survey the progress that has been made in the topic since 1988.

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