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چکیده
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Let S = K[x_1, . . . , x_n] be a polynomial ring over a field K. In this paper, we give some results for sum, product and colon of clean (pretty clean) monomial ideals. We also generalize Soleyman Jahan’s result from monomial ideals with at most 3 variables to monomial ideals with number of arbitrary variables. Indeed, we prove that if I = uJ is a monomial ideal of S, where u is a monomial in S, and J is a monomial ideal of height >= 2, then I is pretty clean if and only if J is pretty clean.
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