A graded subring of an inverse limit of polynomial rings

We study the power series ring R= K[[x1,x2,x3,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R. Of particular interest are the homogeneous, finitely generated ideals in R', among them the generic ideals. The definition of S as an inverse limit yields a set of truncation homomorphisms from S to K[x1,...,xn] which restrict to R'. We have that the truncation of a generic I in R' is a generic ideal in K[x1,...,xn]. It is shown in Initial ideals of Truncated Homogeneous Ideals that the initial ideal of such an ideal converge to the initial ideal of the corresponding ideal in R'. This initial ideal need no longer be finitely generated, but it is always locally finitely generated: this is proved in Gröbner Bases in R'. We show in Reverse lexicographic initial ideals of generic ideals are finitely generated that the initial ideal of a generic ideal in R' is finitely generated. This contrast to the lexicographic term order. If I in R' is a homogeneous, locally finitely generated ideal, and if we write the Hilbert series of the truncated algebras K[x1,...,xn] module the truncation of I as qn(t)/(1-t)n, then we show in Generalized Hilbert Numerators that the qn's converge to a power series in t which we call the generalized Hilbert numerator of the algebra R'/I. In Gröbner bases for non-homogeneous ideals in R' we show that the calculations of Gröbner bases and initial ideals in R' can be done also for some non-homogeneous ideals, namely those which have an associated homogeneous ideal which is locally finitely generated. The fact that S is an inverse limit of polynomial rings, which are naturally endowed with the discrete topology, provides S with a topology which makes it into a complete Hausdorff topological ring. The ring R', with the subspace topology, is dense in R, and the latter ring is the Cauchy completion of the former. In Topological properties of R' we show that with respect to this topology, locally finitely generated ideals in R'are closed.

Land, Power and Technology : Essays on Political Economy and Historical Development

Land Ownership and Development: Evidence from Postwar Japan This paper analyzes the effect of land ownership on technology adoption and structural transformation. A large-scale land reform in postwar Japan enforced a large number of tenant farmers who were cultivating land to become owners of this land. I find that the municipalities which had many owner farmers after the land reform tended to experience a quick entry of new agricultural machines which became available after the reform. The adoption of the machines reduced the dependence on family labor, and led to a reallocation of labor from agriculture to industries and service sectors in urban centers when these sectors were growing. I also analyze the aggregate impact of labor reallocation on economic growth by using a simple growth model and micro data. I find that it increased GDP by about 12 percent of the GDP in 1974 during 1955-74. I also find a large and positive effect on agricultural productivity. Loyalty and Treason: Theory and Evidence from Japan's Land Reform A historically large-scale land reform in Japan after World War II enforced by the occupation forces redistributed a large area of farmlands to tenant farmers. The reform demolished hierarchical structures by weakening landlords' power in villages and towns. This paper investigates how the change in the social and economic structure of small communities affects electoral outcomes in the presence of clientelism. I find that there was a considerable decrease in the vote share of conservative parties in highly affected areas after the reform. I find the supporting evidence that the effect was driven by the fact that the tenant farmers who had obtained land exited from the long-term tenancy contract and became independent landowners. The effect was relatively persistent. Finally, I also find the surprising result that there was a decrease, rather than an increase, in turnout in these areas after the reform.  Geography and State Fragmentation We examine how geography affects the location of borders between sovereign states in Europe and surrounding areas from 1500 until today at the grid-cell level. This is motivated by an observation that the richest places in this region also have the highest historical border presence, suggesting a hitherto unexplored link between geography and modern development, working through state fragmentation. The raw correlations show that borders tend to be located on mountains, by rivers, closer to coasts, and in areas suitable for rainfed, but not irrigated, agriculture. Many of these patterns also hold with rigorous spatial controls. For example, cells with more rivers and more rugged terrain than their neighboring cells have higher border densities. However, the fragmenting effects of suitability for rainfed agriculture are reversed with such neighbor controls. Moreover, we find that borders are less likely to survive over time when they separate large states from small, but this size-difference effect is mitigated by, e.g., rugged terrain.