TY - JOUR
T1 - Matrix and Polynomial Reversibility of Rings
AU - Veldsman, Stefan
N1 - Publisher Copyright:
© 2015, Taylor & Francis Group, LLC.
PY - 2015/4/3
Y1 - 2015/4/3
N2 - Reversibility of rings is a generalization of commutativity, but more than often, this weaker commutativity is a consequence of the absence of certain zero products. For example, a reversible ring is prime if and only if it is an integral domain, and a ring is reduced if and only if it is reversible and semiprime. Here we define and investigate classes of more restricted reversible rings which fulfill stronger commutative requirements, for example, rings that satisfy ab = 0 = ac + db implies ba = 0 = ca + bd.
AB - Reversibility of rings is a generalization of commutativity, but more than often, this weaker commutativity is a consequence of the absence of certain zero products. For example, a reversible ring is prime if and only if it is an integral domain, and a ring is reduced if and only if it is reversible and semiprime. Here we define and investigate classes of more restricted reversible rings which fulfill stronger commutative requirements, for example, rings that satisfy ab = 0 = ac + db implies ba = 0 = ca + bd.
KW - Mat-k-reversible ring
KW - Mat-reversible
KW - Poly-k-reversible ring
KW - Poly-reversible
KW - Reversible ring
KW - Strongly reversible
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U2 - 10.1080/00927872.2013.867969
DO - 10.1080/00927872.2013.867969
M3 - Article
AN - SCOPUS:84923269165
SN - 0092-7872
VL - 43
SP - 1571
EP - 1582
JO - Communications in Algebra
JF - Communications in Algebra
IS - 4
ER -