【摘 要】
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Let A be a ring.In this paper we generalize some results introduced by Aliabad and Mohamadian.We give a relation between the z-ideals of A and those of the form
【机 构】
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Faculty of Sciences of Monastir, Monastir, Tunisia
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Let A be a ring.In this paper we generalize some results introduced by Aliabad and Mohamadian.We give a relation between the z-ideals of A and those of the formal power series rings in an infinite set of indeterminates over A.Consider A[[XA]]3 and its subrings A[[XΛ]]1,A[[XΛ]]2,and A[[XΛ]]α,where α is an infinite cardinal number.In fact,a z-ideal of the rings defined above is of the form I + (XΛ)i,where i =1,2,3 or an infinite cardinal number and I is a z-ideal of A.In addition,we prove that the same condition given by Aliabad and Mohamadian can be used to get a relation between the minimal prime ideals of the ring of the formal power series in an infinite set of indeterminates and those of the ring of coefficients.As a natural result,we get a relation between the z°-ideals of the formal power series ring in an infinite set of indeterminates and those of the ring of coefficients.
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