be a commutative Noetherian ring and
be an ideal of
has the strong persistence property if
. Also, we say that
symbolic strong persistence property if
symbolic power of
. In this paper, by using some monomial
operations, such as expansion, weighting, monomial multiple,
monomial localization, and contraction, we introduce several
methods for constructing new monomial ideals which have the
symbolic strong persistence property based on the monomial ideals
which have the symbolic strong persistence property. We also probe
the strong persistence property of the cover ideal of the union of
two finite simple graphs.
Key Words: Strong persistence property, associated
primes, cover ideals, symbolic strong persistence property.
2010 Mathematics Subject Classification: Primary
13C13, 13B25, 13A30, 05E40; Secondary 13P25, 05C25.
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