Geodesic
GENERALISED ARMENDARIZ PROPERTIES OF CROSSED PRODUCT TYPE
Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 313-323

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DOI

Let R be a ring and M a monoid with twisting f:M × M → U(R) and action ω: M→ Aut(R). We introduce and study the concepts of CM-Armendariz and CM-quasi-Armendariz rings to generalise various Armendariz and quasi-Armendariz properties of rings by working on the context of the crossed product R*M over R. The following results are proved: (1) If M is a u.p.-monoid, then any M-rigid ring R is CM-Armendariz; (2) if I is a reduced ideal of an M-compatible ring R with M a strictly totally ordered monoid, then R/I being CM-Armendariz implies that R is CM-Armendariz; (3) if M is a u.p.-monoid and R is a semiprime ring, then R is CM-quasi-Armendariz. These results generalise and unify many known results on this subject. 
ZHAO, LIANG; ZHOU, YIQIANG. GENERALISED ARMENDARIZ PROPERTIES OF CROSSED PRODUCT TYPE. Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 313-323. doi: 10.1017/S001708951500021X
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     author = {ZHAO, LIANG and ZHOU, YIQIANG},
     title = {GENERALISED {ARMENDARIZ} {PROPERTIES} {OF} {CROSSED} {PRODUCT} {TYPE}},
     journal = {Glasgow mathematical journal},
     pages = {313--323},
     year = {2016},
     volume = {58},
     number = {2},
     doi = {10.1017/S001708951500021X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951500021X/}
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