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Vietnam Journal of Mathematics 40:1 (2012)
107-115
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Remarks on Rings with Zero Products
Commuting and Zero Insertion Properties
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Zhanping Wang
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Department of Mathematics, Northwest Normal
University,
Lanzhou, 730070, China
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Received August 15, 2011
Revised December 6, 2011
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Abstract. In this paper, we continue to study the
rings satisfying zero insertion property for n (abbr., ZIn)
and zero products commuting property for n (abbr., ZCn).
In particular, we prove that R
satisfies ZIn(resp., ZCn) if I is a reduced ideal of R and R/I satisfies ZIn(resp.,
ZCn), where n is a pos-itive integer.
Furthermore, we show that $[[R^{S,\leq}]]$ satisfies ZIn(resp., ZCn)
if and only if R s- atisfies ZIn(resp., ZCn) under some
additional conditions.
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2000 Mathematics
Subject Classification. 16U80, 16S70.
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Keywords. Rings
satisfying ZIn, rings
satisfying ZCn, rings
of generalized power series.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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