Weakly Krull and related domains of the form D+M, A+XB[X] and A+X2B[X]

Let T = K + M and R = D + M be integral domains, where K is a field, All is a nonzero maximal ideal of T, and D is a proper subring of K. We show that R. is a weakly Krull domain, respectively, WFD, AWFD, GWFD, if and only if ht M = 1, D is a field, and T is a weakly Krull domain, respectively, WFD, AWFD, GWFD. Let A g B be an extension of integral domains, R = A + XB[X], and D = A + (XB)-B-2[X]. We also show that R is a weakly Krull domain if and only if D is a weakly Krull domain, if and only if BA-{0} is a field, qf(A) boolean AND B = A, and B[X] is a weakly Krull domain; that R is a WFD, respectively AWFD, if and only if qf(A) boolean AND B = A B[X] is a WFD, respectively AWFD, and for each 0 not equal b is an element of B, there is a unit u of B such that ub is an element of A (respectively, an integer n = n(b) >= 1 and a unit u of B such that ub(n) is an element of A); and that if charB not equal 0, then R is an AWFD if and only if D is an AWFD.