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Commutative ideal theory without finiteness conditions: Completely irreducible ideals |
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| Authors: | Laszlo Fuchs William Heinzer Bruce Olberding |
| Institution: | Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 ; Department of Mathematics, Purdue University, West Lafayette, Indiana 47907 ; Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001 |
| Abstract: | An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an irredundant intersection of completely irreducible ideals, and we study the question of uniqueness of such representations. We characterize those commutative rings in which every ideal is an irredundant intersection of completely irreducible ideals. |
| Keywords: | Irreducible ideal completely irreducible ideal irredundant intersection arithmetical ring |
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