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On Weak Armendariz Rings [PDF]
Bulletin of the Korean Mathematical Society, 2009 In the present note we study the properties of weak Armen- dariz rings, and the connections among weak Armendariz rings, Armen- dariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime
Yang Lee
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Communications in Algebra, 2003
Abstract For a ring endomorphism α, we introduce α-skew Armendariz rings which are a generalization of α-rigid rings and Armendariz rings, and investigate their properties. Moreover, we study on the relationship between the Baerness and p.p.-property of a ring R and these of the skew polynomial ring R[x; α] in case R is α-skew Armendariz.
Tai Keun Kwak
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Abstract For a ring endomorphism α, we introduce α-skew Armendariz rings which are a generalization of α-rigid rings and Armendariz rings, and investigate their properties. Moreover, we study on the relationship between the Baerness and p.p.-property of a ring R and these of the skew polynomial ring R[x; α] in case R is α-skew Armendariz.
Tai Keun Kwak
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Communications in Algebra, 2010
We construct various examples of Armendariz and related rings by reviewing and extending some results concerning the structure of nil(R). In particular, we give some examples of Armendariz rings related to power series rings and an example of an n-Armendariz ring, for all n ≥ 1, which is not Armendariz.
Ramon Antoine
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We construct various examples of Armendariz and related rings by reviewing and extending some results concerning the structure of nil(R). In particular, we give some examples of Armendariz rings related to power series rings and an example of an n-Armendariz ring, for all n ≥ 1, which is not Armendariz.
Ramon Antoine
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Asian-European Journal of Mathematics, 2012
Antoine [Nilpotent elements and Armendariz rings, J. Algebra319 (2008) 3128–3140] studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. When the set of nilpotent elements of a ring R with an α-condition, namely α-compatibility, forms an ideal, we observe that R satisfies a nil Armendariz-type ...
Habibi, M., Moussavi, A.
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Antoine [Nilpotent elements and Armendariz rings, J. Algebra319 (2008) 3128–3140] studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. When the set of nilpotent elements of a ring R with an α-condition, namely α-compatibility, forms an ideal, we observe that R satisfies a nil Armendariz-type ...
Habibi, M., Moussavi, A.
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π-Armendariz Rings and Related Concepts
Baghdad Science JournalIn this paper we investigated some new properties of π-Armendariz rings and studied the relationships between π-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, α-compatible rings and ...
Abduldai, Areej M., Abidali, Roaa M.
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Communications in Algebra, 2006
We introduce weak Armendariz rings which are a generalization of semicommutative rings and Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak Armendariz if and only if for any n, the n-by-n upper triangular matrix ring T n (R) is weak Armendariz.
Renyu Zhao
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We introduce weak Armendariz rings which are a generalization of semicommutative rings and Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak Armendariz if and only if for any n, the n-by-n upper triangular matrix ring T n (R) is weak Armendariz.
Renyu Zhao
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Asian-European Journal of Mathematics, 2009
In this note we introduce a concept, so-called π-Near-Armendariz ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of π-Near-Armendariz rings, constructing typical examples. We next extend the class of π-Near-Armendariz rings, through various ring extensions.
Ghalandarzadeh, Sh., Malakooti Rad, P.
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In this note we introduce a concept, so-called π-Near-Armendariz ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of π-Near-Armendariz rings, constructing typical examples. We next extend the class of π-Near-Armendariz rings, through various ring extensions.
Ghalandarzadeh, Sh., Malakooti Rad, P.
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Extensions of Generalized Armendariz Rings
Algebra Colloquium, 2006A ring R is called Armendariz if whenever the product of any two polynomials in R[x] over R is zero, then so is the product of any pair of coefficients from the two polynomials. Such rings have been extensively studied in literature. For a ring endomorphism α, we introduce the notion of α-Armendariz rings by considering the polynomials in the skew ...
Hong, Chan Yong +2 more
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Generalizations of reversible and Armendariz rings
International Journal of Algebra and Computation, 2016This paper concerns several ring theoretic properties related to matrices and polynomials. The basic properties of [Formula: see text]-reversible and power-Armendariz are studied. We provide a method by which one can always construct a power-Armendariz ring but neither symmetric nor Armendariz from given any symmetric ring. We investigate next various
Juncheol Han +4 more
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