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Miskolc Mathematical Notes, ISSN 1787-2405, 2018, Volume 19, Issue 1, pp. 581 - 590
Let M be a module over a commutative ring R. In this paper we generalize some annihilator conditions on rings to modules. Denote by Nil(M) the set of all... 
Weak Armendariz ring | Weak Armendariz module | Armendariz ring | Armendariz module | MATHEMATICS | weak Armendariz ring | weak Armendariz module
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 10/2017, Volume 16, Issue 10
A ring R is central Armendariz if f(x) = a(0) + a(1)x + ... + a(m)x(m) and g(x) = b(0) + b(1)x + ... + b(n)x(n) over R satisfy f(x) g(x) = 0 then all a(i)b(j)... 
Armendariz rings | central Armendariz rings | weak Armendariz rings | MATHEMATICS | MATHEMATICS, APPLIED | NILPOTENT ELEMENTS
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 2016, Volume 53, Issue 2, pp. 415 - 431
This note is concerned with examining nilradicals and Jacobson radicals of polynomial rings when related factor rings are Armendariz. Especially we elaborate... 
Jacobson radical | Polynomial ring | Nilradical | Feckly armendariz ring | Armendariz ring | MATHEMATICS | MATHEMATICS, APPLIED | feckly Armendariz ring | nilradical | ARMENDARIZ RINGS | polynomial ring | NILPOTENT ELEMENTS
Journal Article
Journal of Algebra, ISSN 0021-8693, 2008, Volume 319, Issue 8, pp. 3128 - 3140
We study the structure of the set of nilpotent elements in Armendariz rings and introduce nil-Armendariz as a generalization. We also provide some new examples... 
Nilpotent elements | Polynomial ring | Nil-Armendariz ring | Armendariz ring | MATHEMATICS | nil-Armendariz ring | REVERSIBLE RINGS | EXTENSIONS | nilpotent elements | polynomial ring
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2017, Volume 41, Issue 6, pp. 1673 - 1686
Let f : A -> B be a ring homomorphism and J be an ideal of B. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of A... 
Amalgamated algebra along an ideal | Reduced ring | Weak Armen-dariz | Nil-Armendariz ring | Armendariz ring | Semicommutative ring | MATHEMATICS | reduced ring | nil-Armendariz ring | RINGS | semicommutative ring | weak Armendariz | DUPLICATION
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 05/2013, Volume 39, Issue 2, pp. 355 - 368
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 06/2015, Volume 14, Issue 5, pp. 1550064 - 1-1550064-21
Antoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced the concept of nil-Armendariz property as a generalization.... 
β-nil-Armendariz ring | skew polynomial ring | α-Armendariz ring | β-nilpotent | polynomial ring | MATHEMATICS | MATHEMATICS, APPLIED | alpha-Armendariz ring | ORE EXTENSIONS | beta-nilpotent | beta-nil-Armendariz ring | REDUCED RINGS | Polynomials | Algebra | Standards | Rings (mathematics)
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 2002, Volume 168, Issue 1, pp. 45 - 52
Let R be a ring and let R[ x] denote the polynomial ring over R. We study relations between the set of annihilators in R and the set of annihilators in R[ x]. 
MATHEMATICS | ARMENDARIZ RINGS | MATHEMATICS, APPLIED
Journal Article
Journal of the Korean Mathematical Society, ISSN 0304-9914, 2010, Volume 47, Issue 3, pp. 455 - 466
For an endomorphism alpha of a ring R, we introduce the weak alpha-skew Armendariz rings which are a generalization of the alpha-skew Armendariz rings and the... 
Weak α-skew Armendariz rings | Weak Armendariz rings | α-skew armendariz rings | Reversible rings | MATHEMATICS | MATHEMATICS, APPLIED | EXTENSIONS | weak alpha-skew Armendariz rings | weak Armendariz rings | reversible rings | alpha-skew Armendariz rings
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 10/2017, Volume 16, Issue 10
Journal Article
Frontiers of Mathematics in China, ISSN 1673-3452, 08/2016, Volume 11, Issue 4, pp. 1017 - 1036
Journal Article
Mathematical Sciences, ISSN 2008-1359, 9/2018, Volume 12, Issue 3, pp. 235 - 242
In this paper, we continue to study properties of skew polynomial ring $$R[x;\alpha ,\delta ]$$ R[x;α,δ] , where R is an associative ring equipped with an... 
16S99 | 16S50 | alpha$$ α | delta$$ δ )-Skew Armendariz | Mathematics | Applications of Mathematics | Weak Armendariz rings | Weak ( $$\alpha$$ α | delta$$ δ )-skew | 16S36 | MATHEMATICS | Weak (alpha . delta)-skew | MATHEMATICS, APPLIED | (alpha . delta)-Skew Armendariz
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 2003, Volume 185, Issue 1, pp. 207 - 223
A ring R is called reversible if ab=0 implies ba=0 for a, b∈ R. We continue in this paper the study of reversible rings by Cohn [4]. We first consider... 
MATHEMATICS | REPRESENTATION | MATHEMATICS, APPLIED | ARMENDARIZ RINGS | IDEALS
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2016, Volume 13, Issue 6, pp. 4723 - 4744
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 03/2018, Volume 17, Issue 3
The purpose of this paper is to provide useful connections between units and zero divisors, by investigating the structure of a class of rings in which Kothe's... 
unit | Armendariz ring | matrix ring | IFP ring | nilpotent element | polynomial ring | Unit-IFP ring | MATHEMATICS, APPLIED | REVERSIBLE RINGS | EXTENSIONS | POWER-SERIES RINGS | EXAMPLES | MATHEMATICS | ARMENDARIZ RINGS
Journal Article
Asian-European Journal of Mathematics, ISSN 1793-5571, 03/2011, Volume 4, Issue 1, pp. 81 - 94
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 6/2010, Volume 81, Issue 3, pp. 361 - 397
Let R be a ring, S a strictly ordered monoid, and omega:S -> End(R) a monoid homomorphism. The skew generalized power series ring R[[S, omega]] is a common... 
semicommutative | (S,)-Armendariz | 2-primal | reversible | reduced | uniserial | skew generalized power series ring | 2-PRIMAL RINGS | EXTENSIONS | PROPERTY | QUESTIONS | MATHEMATICS | SKEW POLYNOMIAL-RINGS | POWER-SERIES | (S, omega)-Armendariz
Journal Article
Carpathian Journal of Mathematics, ISSN 1584-2851, 1/2016, Volume 32, Issue 2, pp. 251 - 258
Let 𝑅 be a ring with the set of nilpotents Nil(𝑅). We prove that the following are equivalent: (i) Nil(𝑅) is additively closed, (ii) Nil(𝑅) is... 
Integers | Equivalence relation | Algebra | Mathematical theorems | Boolean data | Mathematical rings | Polynomials | Subrings | Nilpotent | Exchange ring | Strongly nil clean ring | Armendariz ring | NR ring | NIL | MATHEMATICS | strongly nil clean ring | ARMENDARIZ | MATHEMATICS, APPLIED | exchange ring
Journal Article
Asian-European Journal of Mathematics, ISSN 1793-5571, 03/2016, Volume 9, Issue 1
Journal Article
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