In the 1960s Bruno Buchberger presented his first critical-pair-completion algorithm, now called Buchberger’s algorithm. Since then Gröbner bases have become a powerful tool in computational algebra and algebraic geometry. What is not as well known is that Buchberger (1985, 1987) has also shown a way of computing Gröbner bases in the integers. This is not as trivial as it may seem. In the polyn...

for any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. the condition is that every minimal ideal of the ring consist entirely of bounded elements. it is not too stringent, and is satisfied, for instance, by rings of conti...

coexisting ankylosing spondylitis and hereditary multiple exostoses have rarely been reported (three patients) previously. a 27-year-old man with hereditary multiple exostoses is presented as a fourth report. at the age of 15 years, the patient had multiple exostoses around the knee, ankle and shoulder joints. he was diagnosed with ankylosing spondylitis 3 years ago. the patient’s sister and hi...

background: neonates affected by hereditary spherocytosis may suffer from significant jaundice. this study was conducted on neonates with jaundice hospitalized at the children’s hospital in bandar abbas, south iran, to determine the frequency of hereditary spherocytosis among them. patients and methods: in this cross-sectional study, 814 neonates with jaundice hospitalized at the children’s hos...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

the hereditary ataxias comprise a wide spectrum of heterogeneous disorders that share three features: ataxia, involvement of cerebellum or its connections, and heritability. in many hereditary ataxias, the underlying gene mutations have been identified. knowledge of the causative mutations allows a rational classification of hereditary ataxias as autosomal recessive, autosomal dominant or mater...