ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS

By Chan Huh, Yang Lee, Agata Smoktunowicz. 2002

284 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/225ac440a9bccdfb7373bd9912c9aa2a515acf83

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. C. Hong
2. Yiqiang Zhou
3. Tsiu-Kwen Lee
4. Pace P. Nielsen
5. Yang Lee
6. Nam Kyun Kim
7. Zhong-kui Liu
8. Renyu Zhao

In Computational Theory and Mathematics

1. Pace P. Nielsen
2. Yiqiang Zhou
3. Zhong-kui Liu

Citations in the corpus

• On Weak Armendariz Rings (2006, background): “(Huh et al., 2002, Example 14) Let F be a field and A = F a b c be the free algebra of polynomials with zero constant terms in noncommuting indeterminates a b c over F .”
• Rings with Property (A) and their extensions (2007, background): “But by [11, Example 2], there exists a semicommutative ring whose polynomial rings are not semicommutative.”
• Armendariz and Reduced Rings (2004, background): “…1974, Armendariz (1974) noted that every reduced ring is Armendariz, but the more comprehensive study of the notion of Armendariz rings was carried out just recently (see Anderson and Camillo, 1998; Hirano, 2002; Huh et al., 2002; Kim and Lee, 2000; Lee and Wong, 2003; Rege and Chhawchharia, 1997).”
• A taxonomy of 2-primal rings (2003, unknown): “Smoktunowicz; see [15,25,29], and [48].”
• Power Series Rings Satisfying a Zero Divisor Property (2006, background): “Based on this result, nonreduced Armendariz rings were studied by Anderson and Camillo (1998), Hirano (2002), Huh et al. (2002), Kim and Lee (2000), Rege and Chhawchharia (1997), and so on.”
• Semi-commutativity and the McCoy condition (2006, background): “(2) and (3) we reach the same contradiction as before.”
• A UNIFIED APPROACH TO VARIOUS GENERALIZATIONS OF ARMENDARIZ RINGS (2010, unknown): “The second part of the result generalizes [17, Lemma 7], [15, Corollary 8], and [22, Lemma 3.4].”
• -Clean Rings; Some Clean and Almost Clean Baer -rings and von Neumann Algebras (2010, unknown): “In general, (6) ⇒ (3) ⇒ (2) ⇒ (1), (6) ⇒ (5) ⇒ (2), and (5) ⇒ (4) ⇒ (1), and each of the implications is strict (see [10], [18] [17] and [11]).”