on the structure of algebraic algebras and related rings
... Our starting point is the observation that if a semi-simple /-ring contains a nilpotent element a of index m, then the ideal generated by a contains a system of m2 matrix units. One of the consequences is then the following result: If 5 is a semi-simple Ii-ring (i.e., an J-ring with bounded index), ...
... Our starting point is the observation that if a semi-simple /-ring contains a nilpotent element a of index m, then the ideal generated by a contains a system of m2 matrix units. One of the consequences is then the following result: If 5 is a semi-simple Ii-ring (i.e., an J-ring with bounded index), ...
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The Pontryagin
... Theorem 1 (Stable Pontrjagin-Thom). There is an isomorphism p : πS• → Ωfr• of Z-graded rings. This is a quite different, but equivalent, perspective on πS• , and as such is quite useful: it’s completely geometric, unlike the very abstract stable homotopy groups. The proof has five main steps. (1) Fi ...
... Theorem 1 (Stable Pontrjagin-Thom). There is an isomorphism p : πS• → Ωfr• of Z-graded rings. This is a quite different, but equivalent, perspective on πS• , and as such is quite useful: it’s completely geometric, unlike the very abstract stable homotopy groups. The proof has five main steps. (1) Fi ...
Commutative Algebra I
... multiplication) satisfying the following conditions: (1) (R, +) is an abelian group, (2) multiplication is associative, i.e., for all elements x, y, and z in R, x(yz) = (xy)z, and distributive over addition, i.e., for all x, y, and z in R, we have x(y + z) = xy + xz and (y + z)x = yx + zx. We shall ...
... multiplication) satisfying the following conditions: (1) (R, +) is an abelian group, (2) multiplication is associative, i.e., for all elements x, y, and z in R, x(yz) = (xy)z, and distributive over addition, i.e., for all x, y, and z in R, we have x(y + z) = xy + xz and (y + z)x = yx + zx. We shall ...
THE MOVING CURVE IDEAL AND THE REES
... generators gives the implicit equation when n = 4 and µ = 2. • (Commutative Algebra) In 1997, Jouanolou proved that if p and q are forms of degree 2 in s, t whose coefficients are variables, then the above procedure computes the minimal generators of the saturation of hp, qi with respect to hs, ti ( ...
... generators gives the implicit equation when n = 4 and µ = 2. • (Commutative Algebra) In 1997, Jouanolou proved that if p and q are forms of degree 2 in s, t whose coefficients are variables, then the above procedure computes the minimal generators of the saturation of hp, qi with respect to hs, ti ( ...
189 ON WEAKLY REVERSIBLE RINGS Throughout this paper, all
... [1], a ring R is called reversible if ab = 0 implies ba = 0 for a, b ∈ R. AndersonCamillo [2], observing the rings whose zero products commute, used the term ZC2 for what is called reversible; while Krempa-Niewieczerzal [3] took the term C0 for it. A generalization of reversible rings is investigate ...
... [1], a ring R is called reversible if ab = 0 implies ba = 0 for a, b ∈ R. AndersonCamillo [2], observing the rings whose zero products commute, used the term ZC2 for what is called reversible; while Krempa-Niewieczerzal [3] took the term C0 for it. A generalization of reversible rings is investigate ...
The rule of induction in the three variable arithmetic
... Theorem 1 was proved by Shoenfield ; theorem 2 will be proved here. Since it is routine to show that B1 - 4 (B1- 7, C’d respectively) are provable from A 1 - 5 (A 1 - 7) by RIO applied to formulae in 0,’ , P, + only ( 0,’ P, +, ’) these theorems are all that is needed to give the equivalences referr ...
... Theorem 1 was proved by Shoenfield ; theorem 2 will be proved here. Since it is routine to show that B1 - 4 (B1- 7, C’d respectively) are provable from A 1 - 5 (A 1 - 7) by RIO applied to formulae in 0,’ , P, + only ( 0,’ P, +, ’) these theorems are all that is needed to give the equivalences referr ...
