云顶线上赌博

讲座内容：

A crucial strategy in factorization theory makes use of transfer homomorphisms. In order to study a monoid $H$ (in a given class of monoids) one constructs a transfer homomorphism $\theta \colon H \to B$, where $B$ is simpler (in some aspects), and $\theta$ pulls back the arithmetic results achieved for $B$ to the original monoid of interest $H$. Transfer homomorphisms and, more generally, factorization theory have been extensively studied in the context of domains and cancellative commutative monoids, while much less has been done in the study of rings with non-trivial zero-divisors (here, all rings are commutative and unital).

One approach (though not the only one) to the study of factorization in a ring $R$ with non-trivial zero-divisors is to analyze the associated monoid of regular elements $R^\bullet$, i.e., elements that are not zero-divisors. To carry out such a study effectively, it is often necessary to assume that the set of regular elements is ``sufficiently large'', for instance one can assume that the ring is a Marot ring.  A ring $R$ is Marot if every ideal $I$ of $R$ is generated by its regular elements, i.e., $I=(I\cap R^\bullet) R.$

After providing some background on the factorization theory of domains and rings with zero-divisors, we will establish sufficient conditions on a subring $R$ of a ring $D$ ensuring that the inclusion $R^\bullet \hookrightarrow D^\bullet$ of the respective monoids of regular elements is a transfer homomorphism.