## Prime ideals in commutative rings and in Riesz spaces |

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### Contents

INTRODUCTI ON | 9 |

SOME ELEMENTARY PROPERTIES OF RIESZ SPACES AND | 15 |

MINIMAL PRIME IDEALS IN COMMUTATIVE RINGS AND | 23 |

3 other sections not shown

### Common terms and phrases

According to theorem analogy annihilator condition assume Baer ring base sets Boolean ring commutative regular ring commutative ring commutative semi-prime ring compact converse corollary defined denotes the ideal direct summand disjoint complement distributive lattice element r e exists an element exists an ideal finitely generated ideal following theorem follows from theorem Given the element Hence hk(S holds for Riesz hull-kernel topology hypothesis ideal containing ideal with respect idempotent II(r II(s implies inf(f,g inf(u,v integer maximal ideal maximal multiplicatively closed maximal with respect minimal prime ideal multiplicatively closed set natural number nilpotent non-empty subset non-zero-divisor Note Observe omhulsel-kern open and closed open subsets order ideal priemidealen principal ideal proper ideal properly included r,s e Riesz space ruimte van Riesz satisfies the annihilator strong unit theorem theorem 2.7 tt(A unit element zero element zero-divisor Zorn's lemma