Abstract.
Decompositions of elements into intersections of primal elements and into intersections of p-components are studied in certain lattice-ordered commutative semigroups, by making use of the new development in commutative ideal theory without finiteness conditions, due to Fuchs-Heinzer-Olberding [7]. Several results concerning ideals can be phrased as theorems in ‘abstract ideal theory’.
The intersections we consider are in general not irredundant, and the associated prime elements are not unique. However, one can establish a canonical intersection that is often irredundant with uniquely determined associated primes.
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Fuchs, L., Reis, R. On lattice-ordered commutative semigroups. Algebra univers. 50, 341–357 (2003). https://doi.org/10.1007/s00012-003-1845-x
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DOI: https://doi.org/10.1007/s00012-003-1845-x