sigma$-Prime Spectrum of Almost Distributive Lattices
For each $\alpha$-ideal of an almost distributive lattice (ADL) to become a $\sigma$-ideal, a set of equivalent conditions is derived, which tends to result in a characterization of generalized Stone ADLs. On an ADL, a one-to-one correspondence is derived between the set of all prime $\sigma$-ideal...
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Published in | European journal of pure and applied mathematics Vol. 17; no. 2; pp. 1094 - 1112 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
01.04.2024
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Online Access | Get full text |
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Summary: | For each $\alpha$-ideal of an almost distributive lattice (ADL) to become a $\sigma$-ideal, a set of equivalent conditions is derived, which tends to result in a characterization of generalized Stone ADLs. On an ADL, a one-to-one correspondence is derived between the set of all prime $\sigma$-ideals of the ADL and the set of all prime $\sigma$-ideals of the quotient ADL. Finally, proved some properties of prime $\sigma$-ideals of a normal ADL topologically. |
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ISSN: | 1307-5543 1307-5543 |
DOI: | 10.29020/nybg.ejpam.v17i2.5098 |