We consider the following condition (*) on an associative ring R : (*). There exists a function f from R into R such that f is a group homomorphism of (R,+), f is injective on R2, and f(xy) = (xy)n(x,y) for some positive integer n(x,y) > 1. Commutativity and structure are established for Artinian rings R satisfying (*), and a counterexample is given for nonArtinian rings. The results generalize...

Subdirectly irreducible non-idempotent groupoids satisfying x · xy = y and x · yz = xy · xz are studied.

Background When gonadal sex reversal occurs in mammalian species, the resultant XX males and XY females become infertile or subfertile, suggesting critical roles of sex chromosomes in germ cell differentiation. The objective of our study is to clarify the mechanism of infertility in the B6.YTIR (XY) sex-reversed female mouse, which can be attributed to a failure in the second meiotic division i...

When XX germ cells develop in a testis they become spermatogenic. Thus, somatic signals determine the sex of genetically female germ cells. In contrast, XY germ cells experimentally transferred to an ovary do not differentiate oogenic cells. Because such cells show some male characteristics when analyzed in adults, it was assumed that XY germ cells autonomously become spermatogenic. Recently, h...

Looking-time studies examined whether 11-month-old infants can individuate two pairs of objects using only shape information. In order to test individuation, the object pairs were presented sequentially. Infants were familiarized either with the sequential pairs, disk-triangle/disk-triangle (XY/XY), whose shapes differed within but not across pairs, or with the sequential pairs, disk-disk/trian...

Many authors have studied methods of generalising Steiner quasigroups by using certain cycle systems. The usual aims have been to preserve the law (xy)y = x, by using the standard construction, or to preserve the law xy = yx, by using the opposite vertex construction. In this paper we seek to generalise the law (xy)y = x to laws of the form ( ... (xy)y . . . )y = x and (y( ... (y(yx)) ... ) = x...