Article Details : |
| | Article Name : | | On Linearly S-Quasi-Armendariz Rings | Author Name : | | ELTIYEB ALI, AYOUB ELSHOKRY | Publisher : | | Bridge Center | Article URL : | | | Abstract : | | Let
R
be a ring,
(S,?)
a strictly ordered monoid.
Properties of the ring
?? ??
S,? R
of generalized power series with
coefficients in
R
and exponents in
S
are considered in this
paper. We devoted to introduce and study linearly
S -quasiArmendariz ring, which is unify the notions of linearly
S -
Armendariz ring and S-quasi-Armendariz ring. It is shown
that, if
R
is linearly
S -quasi-Armendariz ring,
U
is a
nonempty subset in
R
is a two-sided ideal of
R , A l (U) ?
R
for all
s ? S
, then
A
R
is linearly
S -quasi-Armendariz. Also, we prove
that,
R
is semiprime if and only if
R
is reduced linearly
S -
quasi-Armendariz. Moreover, a necessary and sufficient
conditions are given for rings under which the classical left ring
of quotients of
R
, is linearly
S -quasi-Armendariz. | Keywords : | | generalized power series ring, linearly
S -quasiArmendariz ring, semicommutative ring. |
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