Prime and maximal ideals in polynomial rings
... 3. Maximal ideals generated by poynomials of minimal degree. As we have seen in Section 1, if P is an R-disjoint prime ideal of R[X], then P is determined by just one polynomial of minimal degree in P. However, it is well-known that P is not necessarily generated by its polynomials of minimal degree ...
... 3. Maximal ideals generated by poynomials of minimal degree. As we have seen in Section 1, if P is an R-disjoint prime ideal of R[X], then P is determined by just one polynomial of minimal degree in P. However, it is well-known that P is not necessarily generated by its polynomials of minimal degree ...
generalized polynomial identities and pivotal monomials
... generated by all a(r), where the a(x) are generalized monomials including the a¡ with evident restrictions—we show that possessing such a pivotal monomial is a necessary and sufficient condition for a primitive ring to possess a left minimal ideal. The generalization of this result in [l] obtained b ...
... generated by all a(r), where the a(x) are generalized monomials including the a¡ with evident restrictions—we show that possessing such a pivotal monomial is a necessary and sufficient condition for a primitive ring to possess a left minimal ideal. The generalization of this result in [l] obtained b ...
UNIVERSITY OF BUCHAREST FACULTY OF MATHEMATICS AND COMPUTER SCIENCE ALEXANDER POLYNOMIALS OF THREE
... lucrările lui Poincare, Alexander si Dehn. În anul 1928 este introdus pentru prima data aşa numitul polinom Alexander. Acest invariant, este suficient de puternic pentru a detecta diferenţe inaccesibile fără el, dar totodată relativ limitat: de exemplu nu poate detecta diferenţa dintre două ...
... lucrările lui Poincare, Alexander si Dehn. În anul 1928 este introdus pentru prima data aşa numitul polinom Alexander. Acest invariant, este suficient de puternic pentru a detecta diferenţe inaccesibile fără el, dar totodată relativ limitat: de exemplu nu poate detecta diferenţa dintre două ...
COMPUTING THE SMITH FORMS OF INTEGER MATRICES AND
... A + U V is very likely to be the ith invariant factor of A (the ith diagonal entry of the Smith form of A). For this perturbation, a number of repetitions are required to achieve a high probability of correctly computing the ith invariant factor. Each distinct invariant factor can be found through ...
... A + U V is very likely to be the ith invariant factor of A (the ith diagonal entry of the Smith form of A). For this perturbation, a number of repetitions are required to achieve a high probability of correctly computing the ith invariant factor. Each distinct invariant factor can be found through ...
Sicherman Dice
... ever do by hand. It is relatively straightforward to create a program that will generate all of the possible dice labels that could potentially result in the standard probability of sums. Using some reasonable deduction and simple number theory, you can reduce the number of possibilities. The small ...
... ever do by hand. It is relatively straightforward to create a program that will generate all of the possible dice labels that could potentially result in the standard probability of sums. Using some reasonable deduction and simple number theory, you can reduce the number of possibilities. The small ...
A LOWER BOUND FOR AVERAGE VALUES OF DYNAMICAL
... K = log R(F ) = r(F ) = 0, and (2.4) just says that Dϕ (z1 , . . . , zN ) ≥ 0, which of course already follows from Remark 1.10. 2.2. Proof of Theorem 2.1.QAn outline of the proof of Theorem 2.1 is as follows. First, we express i6=j |(xi , yi ) ∧ (xj , yj )| as the determinant of a Vandermonde matr ...
... K = log R(F ) = r(F ) = 0, and (2.4) just says that Dϕ (z1 , . . . , zN ) ≥ 0, which of course already follows from Remark 1.10. 2.2. Proof of Theorem 2.1.QAn outline of the proof of Theorem 2.1 is as follows. First, we express i6=j |(xi , yi ) ∧ (xj , yj )| as the determinant of a Vandermonde matr ...
MIDY`S THEOREM FOR PERIODIC DECIMALS Joseph Lewittes
... Note that (iii) explains the difference between 1/77 where k = 3 and gcd(77, 103 −1) = 1, which has the Midy property (1), and 1/803 where k = 4 and gcd(803, 104 − 1) = 11, for which (1) fails. Various authors have given proofs of this theorem, or parts of it, most being unaware of Midy; see, for ex ...
... Note that (iii) explains the difference between 1/77 where k = 3 and gcd(77, 103 −1) = 1, which has the Midy property (1), and 1/803 where k = 4 and gcd(803, 104 − 1) = 11, for which (1) fails. Various authors have given proofs of this theorem, or parts of it, most being unaware of Midy; see, for ex ...
Parametric Integer Programming in Fixed Dimension
... In its general form, PILP belongs to the second level of the polynomial hierarchy and is Π2 complete; see (Stockmeyer, 1976) and (Wrathall, 1976). Kannan (1990) presented a polynomial algorithm to decide the sentence (1) in the case when n, p and the affine dimension of Q are fixed. This result was ...
... In its general form, PILP belongs to the second level of the polynomial hierarchy and is Π2 complete; see (Stockmeyer, 1976) and (Wrathall, 1976). Kannan (1990) presented a polynomial algorithm to decide the sentence (1) in the case when n, p and the affine dimension of Q are fixed. This result was ...
Geometry of Cubic Polynomials - Exhibit
... theorem of algebra gives us a good starting point. Given an arbitrary polynomial: Fundamental Theorem of Algebra. Any polynomial of degree n has exactly n roots. The polynomial is assumed to have complex coefficients and the roots are complex as well. Generally, these roots are distinct, but not nec ...
... theorem of algebra gives us a good starting point. Given an arbitrary polynomial: Fundamental Theorem of Algebra. Any polynomial of degree n has exactly n roots. The polynomial is assumed to have complex coefficients and the roots are complex as well. Generally, these roots are distinct, but not nec ...
Solutions Chapters 1–5
... 2. The four group is V = {I, a, b, c} where the product of any two distinct elements from {a, b, c} is the third. Therefore, the correspondence 1 → I, α → a, β → b, γ → c is an isomorphism of C2 × C2 and V . 3. Let C2 = {1, a} with a2 = 1, and C3 = {1, b, b2 } with b3 = 1. Then (a, b) generates C2 × ...
... 2. The four group is V = {I, a, b, c} where the product of any two distinct elements from {a, b, c} is the third. Therefore, the correspondence 1 → I, α → a, β → b, γ → c is an isomorphism of C2 × C2 and V . 3. Let C2 = {1, a} with a2 = 1, and C3 = {1, b, b2 } with b3 = 1. Then (a, b) generates C2 × ...
SOME MAXIMAL FUNCTION FIELDS AND ADDITIVE
... This paper is closely connected with [A-G] and [G-K-M] (see Remarks 3.3 and 3.19). The emphases here is on obtaining explicit equations for maximal function fields F given as in (1.1) above. To obtain such explicit equations we consider the trace map from Fq2n to the subfield Fq and we use it to des ...
... This paper is closely connected with [A-G] and [G-K-M] (see Remarks 3.3 and 3.19). The emphases here is on obtaining explicit equations for maximal function fields F given as in (1.1) above. To obtain such explicit equations we consider the trace map from Fq2n to the subfield Fq and we use it to des ...
