… Ext-vanishing results that follow from Theorem 1.1. For instance, the next result, contained in
Theorem 4.5, shows that the fiber product … generated module over the fiber product R. If Exti …

… fiber product, Tor. All four authors were partially supported by FAPESP-Brazil 2018/05271-6,
2018/05268-5 and CNPq-Brazil 421440/2016-3. RW was partially supported by Simons …

… a fiber product, and give criteria for the construction to be minimal. We then specialize this
result to fiber products … If I, J ⊆ R are Tor-independent ideals, then the star product X ∗R Y is a …

… We say that ϕ is Tor-vanishing if \(\text {Tor}^{R}_{i}(k,\phi )= 0\) for all i. If ϕ is injective, the
… defect of fiber products. We also give a short derivation of the depth of fiber products. The …

… content of the condensable co-products from the torrefaction of oil palm fiber pellets [21]. …
component in the tor-liquid [44]. The water percentage in tor-liquid products of torrefaction of …

… In this section we show our product on Tor is induced by the product on the two-sided bar …
By definition, the composite along the top induces ext in cohomology, and the outer vertical …

… These flax fibers may aid in the sustainability of US … ; new fiber products from linseed straw
in the north). To develop and support a US flax fiber industry requires consist quality fibers for …

… significant factor affecting the bulk density and breaking strength of extruded barley product.
… Extrusion cooking may change the content, composition and physiological effects of dietary …

… Ext for finitely generated modules over a quasi-fiber product ring R; that is, R is a local ring
such that R/(x) is a non-trivial fiber product … the vanishing of Ext without the assumption of Tor-…

… Also, we define a new class of fiber product rings, called large, with contains any fiber product
ring R ×k S, for instance, and we derive some results concerning their Poincaré series and …