| The characteristic of an integral domain is zero or prime | 00758QM6JJ | statement | 13G05 |
| Principal ideal | 00A2EDFT9Q | definition | 13A15 |
| Root of a polynomial | 00EHX6FWC0 | definition | 13F20 |
| Prime ideal | 00MHHZ9SNE | concept | 13A15 |
| Evaluation homomorphism | 0125QVNCFQ | definition | 13F20 |
| Root of a polynomial | 019MA1VTR2 | concept | 13F20 |
| Prime element | 01VH21EV6F | concept | 13A05 |
| Euclidean algorithm in a Euclidean domain | 023VY493K0 | concept | 13F07 |
| Associate elements | 02879QH7BY | concept | 13A05 |
| Free module | 02E1T12PP4 | definition | 16D40, 13C10 |
| Existence of maximal ideals | 02HJYT53F7 | statement | 13A15 |
| Polynomial evaluation | 02MAKWDKGT | concept | 13F20 |
| Ideal generated by a subset | 030TZ0DQWT | definition | 13A15 |
| Commutative ring | 0310REJJY8 | concept | 13A99 |
| Formal power series | 033WGN00BF | concept | 13F25 |
| Freshman's dream | 0396VGFA78 | statement | 13A35 |
| Multiplicity of a root | 03XVP8Q4GY | definition | 13F20 |
| Multiplicity of a root | 047SX3TD69 | concept | 13F20 |
| Divisibility in a commutative ring | 04GNK7K4VP | definition | 13A05 |
| Irreducible element | 052SDEPZH7 | definition | 13A05 |
| Associate elements | 053E86NWVK | definition | 13A05 |
| PID implies UFD | 055HT85T3S | statement | 13F15 |
| The rationals as the field of fractions of the integers | 05K3J8J8T2 | example | 13B30 |
| Finitely generated module | 05QY1VEBYD | concept | 13E15, 16D10 |
| Maximal ideals are prime | 05WAF5T0GZ | statement | 13A15 |
| Coprime ideals | 065CK367F9 | concept | 13A15 |
| Noetherian ring | 0670T59HGE | concept | 13E05 |
| Repeated roots and the derivative | 067F8YVYMH | statement | 13F20 |
| Z[x] is not a principal ideal domain | 06E3AG9TM2 | counterexample | 13F20 |
| Prime ideal | 06HC6HK0Z8 | definition | 13A15 |
| Unique factorisation domain | 06YMXJMXYS | definition | 13F15 |
| Formal power series | 072W67KFYK | definition | 13F25 |
| Polynomials in several variables | 07GNX8GCYP | concept | 13F20 |
| Divisibility in a commutative ring | 07RGNK57ED | concept | 13A05 |
| Product of primitive polynomials is primitive | 08C1NWBNHA | statement | 13F20 |
| Content of a polynomial | 08VV7YJRB7 | definition | 13F20 |
| In a PID a nonzero element is irreducible iff it generates a maximal ideal | 095ZHQ7WCJ | statement | 13F10 |
| Ideal | 096Z9MP2ME | concept | 13A15 |
| Maximal ideal | 09J6KGT65G | definition | 13A15 |
| Integral domain | 09S3PFBEPM | definition | 13G05 |
| Module over a ring | 09VDS2W1E8 | definition | 16D10, 13C05 |
| Formal derivative | 0AD4VS02H3 | definition | 13N15 |
| R/P is an integral domain iff P is prime | 0AVXBEC05W | statement | 13A15 |
| R[x] is an integral domain iff R is | 0B5Z1EC66J | statement | 13F20 |
| Monic polynomial | 0BDX4MBKT4 | definition | 13F20 |
| Ring of integers | 0BXA4Q0JHW | statement | 13A99 |
| Monic polynomial | 0C3QBCR46M | concept | 13F20 |
| Polynomials in several variables | 0CES91M79A | definition | 13F20 |
| Irreducible elements need not be prime | 0CHE3J7QMX | counterexample | 13A05 |
| Euclidean domain | 0CHS7RBD39 | concept | 13F07 |
| Principal ideal domain | 0CMD0BCH8T | concept | 13F10 |
| Polynomial ring over a UFD is a UFD | 0D6KH8Y59N | statement | 13F15 |
| Degree of a polynomial | 0DPF6WRZW6 | definition | 13F20 |
| K[x] is a Euclidean domain | 0DQG39K2NH | statement | 13F07 |
| Universal property of the polynomial ring | 0DQMDSVSXJ | statement | 13F20 |
| Free module | 0DZ9DKAKZR | concept | 16D40, 13C10 |
| A finite integral domain is a field | 0EBE031B8E | statement | 13G05 |
| Formal derivative | 0EGN1E1JPB | concept | 13N15 |
| Prime elements are irreducible in an integral domain | 0F0K8DB9TD | statement | 13A05 |
| Field of fractions | 0F2PTGX1A2 | concept | 13B30 |
| Characteristic of a ring | 0F6ES3BRYP | concept | 13A99 |
| Greatest common divisor in an integral domain | 0F7KNJ1ZYN | definition | 13A05 |
| Evaluation homomorphism | 0FCCDXH97W | concept | 13F20 |
| Construction of the rationals as fractions | 0FFH3HSRBA | concept | 13B30 |
| Frobenius endomorphism | 0GHDDVAH8P | definition | 13A35 |
| Euclidean domain | 0GJ2HRG95T | definition | 13F07 |
| Polynomial evaluation | 0GJ7T0NK49 | definition | 13F20 |
| Cancellation in an integral domain | 0GJM24EXP9 | statement | 13G05 |
| Ideal generated by a subset | 0GSW76Q14N | concept | 13A15 |
| Commutative ring | 0GYGHKX834 | definition | 13A99 |
| Product of power series | 0H6KWAYS87 | statement | 13F25 |
| The ring of integers | 0JHM6JK7FD | example | 13A99 |
| Factor theorem | 0K3MWA7DMC | statement | 13F20 |
| Coefficient of a power series | 0M98XYVX6S | definition | 13F25 |
| Sum of ideals | 0MBJVDSK1R | concept | 13A15 |
| Coprime ideals | 0MDJP82TEH | definition | 13A15 |
| Division algorithm for polynomials | 0MES3KS0ZC | statement | 13F20 |
| Prime element | 0MNHXBSX3M | definition | 13A05 |
| Noetherian ring | 0MVH4Y1CRZ | definition | 13E05 |
| Ideal | 0MYSA6MYNA | definition | 13A15 |
| Module over a ring | 0NZ8JA25WK | concept | 16D10, 13C05 |
| Leading coefficient | 0P05RJC5XA | definition | 13F20 |
| Degree of a polynomial | 0P4JRMSWNH | concept | 13F20 |
| Characteristic of a ring | 0P7CH1CND5 | definition | 13A99 |
| Maximal ideal | 0PV74TR5FP | concept | 13A15 |
| Polynomial ring | 0Q9EZS90GY | definition | 13F20 |
| Gauss's lemma | 0QFV5Y1Z5X | statement | 13F20 |
| Euclidean domains are principal ideal domains | 0QKVE1GD9A | statement | 13F07 |
| In a UFD irreducible elements are prime | 0QRCFZKXH8 | statement | 13F15 |
| Integral domain | 0QVD7WBFGN | concept | 13G05 |
| Coefficient of a power series | 0R0D0XY4HT | concept | 13F25 |
| Content of a polynomial | 0R2X8K9QA7 | concept | 13F20 |
| Geometric series as a power series | 0R8JR0ARJ4 | example | 13F25 |
| Principal ideal domain | 0RZYDVZ475 | definition | 13F10 |
| Polynomial ring | 0SDC934R52 | concept | 13F20 |
| Primitive polynomial | 0SP14DZN0G | definition | 13F20 |
| Principal ideal | 0SVYSP8HCG | concept | 13A15 |
| Degree of a product | 0T233AZ1GE | statement | 13F20 |
| Frobenius endomorphism | 0T3WVTD675 | concept | 13A35 |
| Remainder theorem | 0TEDQH56RW | statement | 13F20 |
| Primitive polynomial | 0TXNRQZY0H | concept | 13F20 |
| Leading coefficient | 0V5GYWR8R8 | concept | 13F20 |
| Field of fractions | 0VF11ZTTMD | definition | 13B30 |
| Bézout's identity in a Euclidean domain | 0VY3WPP9Y3 | statement | 13F07 |
| Unique factorisation domain | 0W4X9G6263 | concept | 13F15 |
| Chinese remainder theorem for rings | 0W97J8QED7 | statement | 13A15 |
| R/M is a field iff M is maximal | 0WD3SE7S1X | statement | 13A15 |
| Finitely generated module | 0XHM30WBVB | definition | 13E15, 16D10 |
| Hilbert's basis theorem | 0YKA9J3XEE | statement | 13E05 |
| Irreducible element | 0YMT0D2442 | concept | 13A05 |
| Greatest common divisor in an integral domain | 0ZAF9KHDDF | concept | 13A05 |
