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Connected ring

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Connectedness defines a fairly general class of commutative rings. For example, all
87: 17: 75: 146:(2 ed.), New York: W. H. Freeman and Company, pp. xviii+686, 98:; here the element (1, 0) is a non-trivial idempotent. 35:
that satisfies one of the following equivalent conditions:
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possesses no non-trivial (that is, not equal to 1 or 0)
192: 110:, connectedness is generalized to the concept of a 212: 8: 219: 205: 86:are connected. Non-examples are given by 130: 123: 7: 173: 171: 82:are connected. In particular, all 14: 175: 1: 20:, especially in the field of 191:. You can help Knowledge by 264: 170: 248:Commutative algebra stubs 142:Jacobson, Nathan (1989), 70:Examples and non-examples 187:-related article is a 238:Commutative algebra 185:commutative algebra 44:idempotent elements 22:commutative algebra 108:algebraic geometry 200: 199: 144:Basic algebra. II 80:irreducible rings 255: 221: 214: 207: 179: 172: 164: 134: 128: 112:connected scheme 84:integral domains 59:Zariski topology 30:commutative ring 263: 262: 258: 257: 256: 254: 253: 252: 228: 227: 226: 225: 168: 154: 141: 138: 137: 129: 125: 120: 104: 102:Generalizations 78:and all (meet-) 72: 63:connected space 12: 11: 5: 261: 259: 251: 250: 245: 240: 230: 229: 224: 223: 216: 209: 201: 198: 197: 180: 166: 165: 152: 136: 135: 122: 121: 119: 116: 103: 100: 71: 68: 67: 66: 47: 26:connected ring 13: 10: 9: 6: 4: 3: 2: 260: 249: 246: 244: 241: 239: 236: 235: 233: 222: 217: 215: 210: 208: 203: 202: 196: 194: 190: 186: 181: 178: 174: 169: 163: 159: 155: 153:0-7167-1933-9 149: 145: 140: 139: 132: 131:Jacobson 1989 127: 124: 117: 115: 113: 109: 101: 99: 97: 94: ×  93: 89: 88:product rings 85: 81: 77: 69: 64: 60: 56: 52: 48: 45: 41: 38: 37: 36: 34: 31: 27: 23: 19: 193:expanding it 182: 167: 143: 126: 105: 95: 91: 73: 54: 39: 32: 25: 15: 243:Ring theory 76:local rings 18:mathematics 232:Categories 118:References 57:with the 133:, p 418. 90:such as 51:spectrum 162:1009787 160:  150:  183:This 61:is a 28:is a 189:stub 148:ISBN 49:the 24:, a 106:In 53:of 16:In 234:: 158:MR 156:, 114:. 220:e 213:t 206:v 195:. 96:Z 92:Z 65:. 55:A 46:; 40:A 33:A

Index

mathematics
commutative algebra
commutative ring
idempotent elements
spectrum
Zariski topology
connected space
local rings
irreducible rings
integral domains
product rings
algebraic geometry
connected scheme
Jacobson 1989
ISBN
0-7167-1933-9
MR
1009787
Stub icon
commutative algebra
stub
expanding it
v
t
e
Categories
Commutative algebra
Ring theory
Commutative algebra stubs

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