Add to ORKGVersion 0.0 Abstract. Continuing the study of divisibility theory of arithmetical rings started in [1] and [2] we show that the divisibility theory of arithmetical rings with one minimal prime ideal is axiomatizable as Bezout monoids with one minimal m-prime filter. In particular, every Bezout monoid with one minimal m-prime filter is order-isomorphic to the partially ordered monoid with respect to inverse inclusion, of principal ideals in a Bezout ring with a smallest prime ideal. Although this result can be considered as a satisfactory answer to the divisibility theory of both semi-hereditary domains and valuation rings, the general representation theory of Bezout monoids is still open. 1
This thesis explores two topics in commutative algebra. The first topicis Betti tables, particularly...
AbstractA commutative ring A with unit is called a pm-ring if every prime ideal of A is contained in...
There are well known algorithms to compute the class group of the maximal order $\mathcal{O}_K$ of a...
Continuing the study of divisibility theory of arithmetical rings started in [1] and [2], we show th...
Abstract. A ubiquitous class of lattice ordered semigroups introduced by Bosbach in 1991, which we w...
Abstract. The multiplicative monoid of principal ideals partially ordered by reverse in-clusion, cal...
We prove that the multiplicative monoid of principal ideals partially ordered by reverse inclusion, ...
We investigate commutative Bezout domains in which any nonzero prime ideal is contained in a fini...
International audienceIt is shown that a commutative B\'{e}zout ring $R$ with compact minimal prime ...
AbstractLet H' be the algebra of bounded analytic functions in the open unit disk. An ideal I in H' ...
Abstract. Recently Yehuda Rav has given the concept of Semi-prime ideals in a general lattice by gen...
AbstractIt is shown that certain classes of Bezout domains have stable range 1, and thus are element...
Summary. The article continues the formalization of the lattice theory (as structures with two binar...
International audienceWe study zero divisors and minimal prime ideals in semirings of characteristic...
These are sketchy lecture notes intended to show that the concepts of divisibility, prime elements a...
This thesis explores two topics in commutative algebra. The first topicis Betti tables, particularly...
AbstractA commutative ring A with unit is called a pm-ring if every prime ideal of A is contained in...
There are well known algorithms to compute the class group of the maximal order $\mathcal{O}_K$ of a...
Continuing the study of divisibility theory of arithmetical rings started in [1] and [2], we show th...
Abstract. A ubiquitous class of lattice ordered semigroups introduced by Bosbach in 1991, which we w...
Abstract. The multiplicative monoid of principal ideals partially ordered by reverse in-clusion, cal...
We prove that the multiplicative monoid of principal ideals partially ordered by reverse inclusion, ...
We investigate commutative Bezout domains in which any nonzero prime ideal is contained in a fini...
International audienceIt is shown that a commutative B\'{e}zout ring $R$ with compact minimal prime ...
AbstractLet H' be the algebra of bounded analytic functions in the open unit disk. An ideal I in H' ...
Abstract. Recently Yehuda Rav has given the concept of Semi-prime ideals in a general lattice by gen...
AbstractIt is shown that certain classes of Bezout domains have stable range 1, and thus are element...
Summary. The article continues the formalization of the lattice theory (as structures with two binar...
International audienceWe study zero divisors and minimal prime ideals in semirings of characteristic...
These are sketchy lecture notes intended to show that the concepts of divisibility, prime elements a...
This thesis explores two topics in commutative algebra. The first topicis Betti tables, particularly...
AbstractA commutative ring A with unit is called a pm-ring if every prime ideal of A is contained in...
There are well known algorithms to compute the class group of the maximal order $\mathcal{O}_K$ of a...